# Properties

 Label 135.1.d.a.134.1 Level $135$ Weight $1$ Character 135.134 Self dual yes Analytic conductor $0.067$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -15 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,1,Mod(134,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.134");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$135 = 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 135.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$0.0673737767055$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.135.1 Artin image: $S_3$ Artin field: Galois closure of 3.1.135.1

## Embedding invariants

 Embedding label 134.1 Character $$\chi$$ $$=$$ 135.134

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{5} +1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{5} +1.00000 q^{8} -1.00000 q^{10} -1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{19} -1.00000 q^{23} +1.00000 q^{25} -1.00000 q^{31} +1.00000 q^{34} +1.00000 q^{38} +1.00000 q^{40} +1.00000 q^{46} +2.00000 q^{47} +1.00000 q^{49} -1.00000 q^{50} -1.00000 q^{53} -1.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{79} -1.00000 q^{80} -1.00000 q^{83} -1.00000 q^{85} -2.00000 q^{94} -1.00000 q^{95} -1.00000 q^{98} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$$.

 $$n$$ $$56$$ $$82$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 1.00000 1.00000
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 1.00000 1.00000
$$9$$ 0 0
$$10$$ −1.00000 −1.00000
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −1.00000
$$17$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0 0
$$19$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ 0 0
$$25$$ 1.00000 1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 1.00000 1.00000
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 1.00000 1.00000
$$39$$ 0 0
$$40$$ 1.00000 1.00000
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 1.00000 1.00000
$$47$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ −1.00000 −1.00000
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$62$$ 1.00000 1.00000
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$80$$ −1.00000 −1.00000
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ −1.00000 −1.00000
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −2.00000 −2.00000
$$95$$ −1.00000 −1.00000
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ −1.00000 −1.00000
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 1.00000 1.00000
$$107$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$108$$ 0 0
$$109$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$114$$ 0 0
$$115$$ −1.00000 −1.00000
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ 1.00000 1.00000
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000 1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −1.00000 −1.00000
$$137$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$152$$ −1.00000 −1.00000
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.00000 −1.00000
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 1.00000 1.00000
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 1.00000 1.00000
$$167$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 1.00000 1.00000
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −1.00000 −1.00000
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 1.00000 1.00000
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$198$$ 0 0
$$199$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$200$$ 1.00000 1.00000
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −2.00000 −2.00000
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 1.00000 1.00000
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −2.00000 −2.00000
$$227$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ 0 0
$$229$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 1.00000 1.00000
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$234$$ 0 0
$$235$$ 2.00000 2.00000
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$242$$ −1.00000 −1.00000
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1.00000 1.00000
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −1.00000 −1.00000
$$249$$ 0 0
$$250$$ −1.00000 −1.00000
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$264$$ 0 0
$$265$$ −1.00000 −1.00000
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$272$$ 1.00000 1.00000
$$273$$ 0 0
$$274$$ 1.00000 1.00000
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ −2.00000 −2.00000
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −2.00000 −2.00000
$$303$$ 0 0
$$304$$ 1.00000 1.00000
$$305$$ −1.00000 −1.00000
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1.00000 1.00000
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 1.00000 1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 1.00000 1.00000
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 1.00000 1.00000
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −1.00000 −1.00000
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 1.00000 1.00000
$$347$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$348$$ 0 0
$$349$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 1.00000 1.00000
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 1.00000 1.00000
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 2.00000 2.00000
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 1.00000 1.00000
$$392$$ 1.00000 1.00000
$$393$$ 0 0
$$394$$ 1.00000 1.00000
$$395$$ −1.00000 −1.00000
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ −2.00000 −2.00000
$$399$$ 0 0
$$400$$ −1.00000 −1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −1.00000 −1.00000
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$422$$ 1.00000 1.00000
$$423$$ 0 0
$$424$$ −1.00000 −1.00000
$$425$$ −1.00000 −1.00000
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 1.00000 1.00000
$$438$$ 0 0
$$439$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 1.00000 1.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 1.00000 1.00000
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −2.00000 −2.00000
$$467$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −2.00000 −2.00000
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.00000 −1.00000
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 1.00000 1.00000
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ −1.00000 −1.00000
$$489$$ 0 0
$$490$$ −1.00000 −1.00000
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 1.00000 1.00000
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 1.00000
$$513$$ 0 0
$$514$$ 1.00000 1.00000
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −2.00000 −2.00000
$$527$$ 1.00000 1.00000
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 1.00000 1.00000
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 2.00000 2.00000
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$542$$ 1.00000 1.00000
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1.00000 −1.00000
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$564$$ 0 0
$$565$$ 2.00000 2.00000
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −1.00000
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 1.00000 1.00000
$$587$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$588$$ 0 0
$$589$$ 1.00000 1.00000
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 1.00000 1.00000
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 1.00000 1.00000
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$618$$ 0 0
$$619$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$632$$ −1.00000 −1.00000
$$633$$ 0 0
$$634$$ 1.00000 1.00000
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.00000 −1.00000
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −1.00000 −1.00000
$$647$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$662$$ −2.00000 −2.00000
$$663$$ 0 0
$$664$$ −1.00000 −1.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −1.00000 −1.00000
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$684$$ 0 0
$$685$$ −1.00000 −1.00000
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −2.00000 −2.00000
$$695$$ 2.00000 2.00000
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 1.00000 1.00000
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −2.00000 −2.00000
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 1.00000 1.00000
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ −2.00000 −2.00000
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 2.00000 2.00000
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 1.00000 1.00000
$$759$$ 0 0
$$760$$ −1.00000 −1.00000
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 1.00000 1.00000
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −1.00000
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −1.00000 −1.00000
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 1.00000 1.00000
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$798$$ 0 0
$$799$$ −2.00000 −2.00000
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 1.00000 1.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$828$$ 0 0
$$829$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$830$$ 1.00000 1.00000
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −1.00000 −1.00000
$$834$$ 0 0
$$835$$ −1.00000 −1.00000
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 1.00000 1.00000
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 1.00000 1.00000
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 1.00000 1.00000
$$849$$ 0 0
$$850$$ 1.00000 1.00000
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 2.00000 2.00000
$$857$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$858$$ 0 0
$$859$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$864$$ 0 0
$$865$$ −1.00000 −1.00000
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −1.00000 −1.00000
$$873$$ 0 0
$$874$$ −1.00000 −1.00000
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 1.00000 1.00000
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 1.00000 1.00000
$$887$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ −2.00000 −2.00000
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 1.00000 1.00000
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 2.00000 2.00000
$$905$$ −1.00000 −1.00000
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$920$$ −1.00000 −1.00000
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ −1.00000 −1.00000
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 1.00000 1.00000
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 1.00000 1.00000
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 0 0
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 1.00000 1.00000
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 1.00000 1.00000
$$977$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$984$$ 0 0
$$985$$ −1.00000 −1.00000
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2.00000 2.00000
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 1.00000 1.00000
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 135.1.d.a.134.1 1
3.2 odd 2 135.1.d.b.134.1 yes 1
4.3 odd 2 2160.1.c.b.1889.1 1
5.2 odd 4 675.1.c.c.26.1 2
5.3 odd 4 675.1.c.c.26.2 2
5.4 even 2 135.1.d.b.134.1 yes 1
9.2 odd 6 405.1.h.a.134.1 2
9.4 even 3 405.1.h.b.269.1 2
9.5 odd 6 405.1.h.a.269.1 2
9.7 even 3 405.1.h.b.134.1 2
12.11 even 2 2160.1.c.a.1889.1 1
15.2 even 4 675.1.c.c.26.2 2
15.8 even 4 675.1.c.c.26.1 2
15.14 odd 2 CM 135.1.d.a.134.1 1
20.19 odd 2 2160.1.c.a.1889.1 1
27.2 odd 18 3645.1.n.e.1619.1 6
27.4 even 9 3645.1.n.d.3239.1 6
27.5 odd 18 3645.1.n.e.809.1 6
27.7 even 9 3645.1.n.d.404.1 6
27.11 odd 18 3645.1.n.e.2834.1 6
27.13 even 9 3645.1.n.d.2024.1 6
27.14 odd 18 3645.1.n.e.2024.1 6
27.16 even 9 3645.1.n.d.2834.1 6
27.20 odd 18 3645.1.n.e.404.1 6
27.22 even 9 3645.1.n.d.809.1 6
27.23 odd 18 3645.1.n.e.3239.1 6
27.25 even 9 3645.1.n.d.1619.1 6
45.2 even 12 2025.1.j.c.701.2 4
45.4 even 6 405.1.h.a.269.1 2
45.7 odd 12 2025.1.j.c.701.1 4
45.13 odd 12 2025.1.j.c.26.1 4
45.14 odd 6 405.1.h.b.269.1 2
45.22 odd 12 2025.1.j.c.26.2 4
45.23 even 12 2025.1.j.c.26.2 4
45.29 odd 6 405.1.h.b.134.1 2
45.32 even 12 2025.1.j.c.26.1 4
45.34 even 6 405.1.h.a.134.1 2
45.38 even 12 2025.1.j.c.701.1 4
45.43 odd 12 2025.1.j.c.701.2 4
60.59 even 2 2160.1.c.b.1889.1 1
135.4 even 18 3645.1.n.e.3239.1 6
135.14 odd 18 3645.1.n.d.2024.1 6
135.29 odd 18 3645.1.n.d.1619.1 6
135.34 even 18 3645.1.n.e.404.1 6
135.49 even 18 3645.1.n.e.809.1 6
135.59 odd 18 3645.1.n.d.809.1 6
135.74 odd 18 3645.1.n.d.404.1 6
135.79 even 18 3645.1.n.e.1619.1 6
135.94 even 18 3645.1.n.e.2024.1 6
135.104 odd 18 3645.1.n.d.3239.1 6
135.119 odd 18 3645.1.n.d.2834.1 6
135.124 even 18 3645.1.n.e.2834.1 6

By twisted newform
Twist Min Dim Char Parity Ord Type
135.1.d.a.134.1 1 1.1 even 1 trivial
135.1.d.a.134.1 1 15.14 odd 2 CM
135.1.d.b.134.1 yes 1 3.2 odd 2
135.1.d.b.134.1 yes 1 5.4 even 2
405.1.h.a.134.1 2 9.2 odd 6
405.1.h.a.134.1 2 45.34 even 6
405.1.h.a.269.1 2 9.5 odd 6
405.1.h.a.269.1 2 45.4 even 6
405.1.h.b.134.1 2 9.7 even 3
405.1.h.b.134.1 2 45.29 odd 6
405.1.h.b.269.1 2 9.4 even 3
405.1.h.b.269.1 2 45.14 odd 6
675.1.c.c.26.1 2 5.2 odd 4
675.1.c.c.26.1 2 15.8 even 4
675.1.c.c.26.2 2 5.3 odd 4
675.1.c.c.26.2 2 15.2 even 4
2025.1.j.c.26.1 4 45.13 odd 12
2025.1.j.c.26.1 4 45.32 even 12
2025.1.j.c.26.2 4 45.22 odd 12
2025.1.j.c.26.2 4 45.23 even 12
2025.1.j.c.701.1 4 45.7 odd 12
2025.1.j.c.701.1 4 45.38 even 12
2025.1.j.c.701.2 4 45.2 even 12
2025.1.j.c.701.2 4 45.43 odd 12
2160.1.c.a.1889.1 1 12.11 even 2
2160.1.c.a.1889.1 1 20.19 odd 2
2160.1.c.b.1889.1 1 4.3 odd 2
2160.1.c.b.1889.1 1 60.59 even 2
3645.1.n.d.404.1 6 27.7 even 9
3645.1.n.d.404.1 6 135.74 odd 18
3645.1.n.d.809.1 6 27.22 even 9
3645.1.n.d.809.1 6 135.59 odd 18
3645.1.n.d.1619.1 6 27.25 even 9
3645.1.n.d.1619.1 6 135.29 odd 18
3645.1.n.d.2024.1 6 27.13 even 9
3645.1.n.d.2024.1 6 135.14 odd 18
3645.1.n.d.2834.1 6 27.16 even 9
3645.1.n.d.2834.1 6 135.119 odd 18
3645.1.n.d.3239.1 6 27.4 even 9
3645.1.n.d.3239.1 6 135.104 odd 18
3645.1.n.e.404.1 6 27.20 odd 18
3645.1.n.e.404.1 6 135.34 even 18
3645.1.n.e.809.1 6 27.5 odd 18
3645.1.n.e.809.1 6 135.49 even 18
3645.1.n.e.1619.1 6 27.2 odd 18
3645.1.n.e.1619.1 6 135.79 even 18
3645.1.n.e.2024.1 6 27.14 odd 18
3645.1.n.e.2024.1 6 135.94 even 18
3645.1.n.e.2834.1 6 27.11 odd 18
3645.1.n.e.2834.1 6 135.124 even 18
3645.1.n.e.3239.1 6 27.23 odd 18
3645.1.n.e.3239.1 6 135.4 even 18