# Properties

 Label 2304.4.a.p.1.1 Level $2304$ Weight $4$ Character 2304.1 Self dual yes Analytic conductor $135.940$ Analytic rank $0$ Dimension $1$ CM discriminant -4 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2304,4,Mod(1,2304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2304, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2304.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2304 = 2^{8} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 2304.a (trivial)

## 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: $$135.940400653$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1152) Fricke sign: $$+1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 2304.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+22.0000 q^{5} +O(q^{10})$$ $$q+22.0000 q^{5} +92.0000 q^{13} +104.000 q^{17} +359.000 q^{25} +130.000 q^{29} -396.000 q^{37} +472.000 q^{41} -343.000 q^{49} -518.000 q^{53} +468.000 q^{61} +2024.00 q^{65} -1098.00 q^{73} +2288.00 q^{85} +176.000 q^{89} +594.000 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 22.0000 1.96774 0.983870 0.178885i $$-0.0572491\pi$$
0.983870 + 0.178885i $$0.0572491\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 92.0000 1.96279 0.981393 0.192012i $$-0.0615011\pi$$
0.981393 + 0.192012i $$0.0615011\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 104.000 1.48375 0.741874 0.670540i $$-0.233937\pi$$
0.741874 + 0.670540i $$0.233937\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 359.000 2.87200
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 130.000 0.832427 0.416214 0.909267i $$-0.363357\pi$$
0.416214 + 0.909267i $$0.363357\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −396.000 −1.75951 −0.879757 0.475424i $$-0.842295\pi$$
−0.879757 + 0.475424i $$0.842295\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 472.000 1.79790 0.898951 0.438048i $$-0.144330\pi$$
0.898951 + 0.438048i $$0.144330\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −343.000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −518.000 −1.34251 −0.671253 0.741229i $$-0.734243\pi$$
−0.671253 + 0.741229i $$0.734243\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 468.000 0.982316 0.491158 0.871071i $$-0.336574\pi$$
0.491158 + 0.871071i $$0.336574\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 2024.00 3.86225
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −1098.00 −1.76043 −0.880214 0.474578i $$-0.842601\pi$$
−0.880214 + 0.474578i $$0.842601\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 2288.00 2.91963
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 176.000 0.209618 0.104809 0.994492i $$-0.466577\pi$$
0.104809 + 0.994492i $$0.466577\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 594.000 0.621769 0.310884 0.950448i $$-0.399375\pi$$
0.310884 + 0.950448i $$0.399375\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −598.000 −0.589141 −0.294570 0.955630i $$-0.595177\pi$$
−0.294570 + 0.955630i $$0.595177\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −1460.00 −1.28296 −0.641480 0.767140i $$-0.721679\pi$$
−0.641480 + 0.767140i $$0.721679\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1328.00 1.10556 0.552778 0.833329i $$-0.313568\pi$$
0.552778 + 0.833329i $$0.313568\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1331.00 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 5148.00 3.68361
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2776.00 −1.73117 −0.865583 0.500766i $$-0.833052\pi$$
−0.865583 + 0.500766i $$0.833052\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 2860.00 1.63800
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −3514.00 −1.93207 −0.966034 0.258415i $$-0.916800\pi$$
−0.966034 + 0.258415i $$0.916800\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 3924.00 1.99471 0.997354 0.0726920i $$-0.0231590\pi$$
0.997354 + 0.0726920i $$0.0231590\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 6267.00 2.85253
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −4082.00 −1.79392 −0.896962 0.442108i $$-0.854231\pi$$
−0.896962 + 0.442108i $$0.854231\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 2860.00 1.17449 0.587243 0.809410i $$-0.300213\pi$$
0.587243 + 0.809410i $$0.300213\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −8712.00 −3.46226
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ −5362.00 −1.99982 −0.999910 0.0134266i $$-0.995726\pi$$
−0.999910 + 0.0134266i $$0.995726\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −1174.00 −0.424589 −0.212295 0.977206i $$-0.568094\pi$$
−0.212295 + 0.977206i $$0.568094\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 10384.0 3.53780
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 9568.00 2.91228
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 2684.00 0.774514 0.387257 0.921972i $$-0.373423\pi$$
0.387257 + 0.921972i $$0.373423\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −7088.00 −1.99292 −0.996460 0.0840693i $$-0.973208\pi$$
−0.996460 + 0.0840693i $$0.973208\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −5310.00 −1.41928 −0.709641 0.704563i $$-0.751143\pi$$
−0.709641 + 0.704563i $$0.751143\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −7546.00 −1.96774
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −8096.00 −1.96504 −0.982519 0.186164i $$-0.940394\pi$$
−0.982519 + 0.186164i $$0.940394\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ −11396.0 −2.64170
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −3406.00 −0.771998 −0.385999 0.922499i $$-0.626143\pi$$
−0.385999 + 0.922499i $$0.626143\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −1316.00 −0.285454 −0.142727 0.989762i $$-0.545587\pi$$
−0.142727 + 0.989762i $$0.545587\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5792.00 1.22961 0.614807 0.788677i $$-0.289234\pi$$
0.614807 + 0.788677i $$0.289234\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 5903.00 1.20151
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 9418.00 1.87783 0.938917 0.344143i $$-0.111831\pi$$
0.938917 + 0.344143i $$0.111831\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 10296.0 1.93294
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 6838.00 1.23485 0.617423 0.786632i $$-0.288177\pi$$
0.617423 + 0.786632i $$0.288177\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 10274.0 1.82033 0.910166 0.414243i $$-0.135954\pi$$
0.910166 + 0.414243i $$0.135954\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 33028.0 5.63712
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 12366.0 1.99887 0.999435 0.0336216i $$-0.0107041\pi$$
0.999435 + 0.0336216i $$0.0107041\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 8964.00 1.37488 0.687438 0.726243i $$-0.258735\pi$$
0.687438 + 0.726243i $$0.258735\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 12848.0 1.93720 0.968598 0.248633i $$-0.0799813\pi$$
0.968598 + 0.248633i $$0.0799813\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −6859.00 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −24156.0 −3.46406
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 6372.00 0.884530 0.442265 0.896884i $$-0.354175\pi$$
0.442265 + 0.896884i $$0.354175\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 11960.0 1.63388
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 374.000 0.0487469 0.0243735 0.999703i $$-0.492241\pi$$
0.0243735 + 0.999703i $$0.492241\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 12564.0 1.58834 0.794168 0.607699i $$-0.207907\pi$$
0.794168 + 0.607699i $$0.207907\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −15880.0 −1.97758 −0.988790 0.149315i $$-0.952293\pi$$
−0.988790 + 0.149315i $$0.952293\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 7146.00 0.863929 0.431964 0.901891i $$-0.357821\pi$$
0.431964 + 0.901891i $$0.357821\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ −13412.0 −1.55264 −0.776319 0.630340i $$-0.782916\pi$$
−0.776319 + 0.630340i $$0.782916\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 37336.0 4.26132
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 4862.00 0.539614 0.269807 0.962914i $$-0.413040\pi$$
0.269807 + 0.962914i $$0.413040\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 3872.00 0.412473
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 10120.0 1.06368 0.531840 0.846845i $$-0.321501\pi$$
0.531840 + 0.846845i $$0.321501\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 16506.0 1.68954 0.844768 0.535132i $$-0.179738\pi$$
0.844768 + 0.535132i $$0.179738\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2318.00 0.234187 0.117093 0.993121i $$-0.462642\pi$$
0.117093 + 0.993121i $$0.462642\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −36432.0 −3.45355
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 13068.0 1.22348
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 13520.0 1.23511
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −13156.0 −1.15928
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −14270.0 −1.24265 −0.621323 0.783555i $$-0.713404\pi$$
−0.621323 + 0.783555i $$0.713404\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1480.00 −0.124453 −0.0622265 0.998062i $$-0.519820\pi$$
−0.0622265 + 0.998062i $$0.519820\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −12167.0 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 43424.0 3.52890
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 24460.0 1.94384 0.971920 0.235311i $$-0.0756109\pi$$
0.971920 + 0.235311i $$0.0756109\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −32120.0 −2.52453
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 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
$$557$$ −8626.00 −0.656186 −0.328093 0.944646i $$-0.606406\pi$$
−0.328093 + 0.944646i $$0.606406\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 29216.0 2.17544
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 4280.00 0.315337 0.157669 0.987492i $$-0.449602\pi$$
0.157669 + 0.987492i $$0.449602\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −3454.00 −0.249206 −0.124603 0.992207i $$-0.539766\pi$$
−0.124603 + 0.992207i $$0.539766\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −24368.0 −1.68748 −0.843738 0.536755i $$-0.819650\pi$$
−0.843738 + 0.536755i $$0.819650\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −17030.0 −1.15585 −0.577927 0.816089i $$-0.696138\pi$$
−0.577927 + 0.816089i $$0.696138\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −29282.0 −1.96774
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −19548.0 −1.28799 −0.643994 0.765031i $$-0.722724\pi$$
−0.643994 + 0.765031i $$0.722724\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −26464.0 −1.72674 −0.863372 0.504569i $$-0.831652\pi$$
−0.863372 + 0.504569i $$0.831652\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 68381.0 4.37638
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −41184.0 −2.61067
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −31556.0 −1.96279
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −14872.0 −0.916394 −0.458197 0.888851i $$-0.651505\pi$$
−0.458197 + 0.888851i $$0.651505\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 33358.0 1.99908 0.999540 0.0303236i $$-0.00965378\pi$$
0.999540 + 0.0303236i $$0.00965378\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 22068.0 1.29856 0.649278 0.760551i $$-0.275071\pi$$
0.649278 + 0.760551i $$0.275071\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 4462.00 0.255568 0.127784 0.991802i $$-0.459214\pi$$
0.127784 + 0.991802i $$0.459214\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 4054.00 0.230145 0.115072 0.993357i $$-0.463290\pi$$
0.115072 + 0.993357i $$0.463290\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ −61072.0 −3.40648
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −47656.0 −2.63505
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 49088.0 2.66763
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −20030.0 −1.07920 −0.539602 0.841920i $$-0.681425\pi$$
−0.539602 + 0.841920i $$0.681425\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −8404.00 −0.445161 −0.222580 0.974914i $$-0.571448\pi$$
−0.222580 + 0.974914i $$0.571448\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 46670.0 2.39073
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 8732.00 0.440005 0.220003 0.975499i $$-0.429393\pi$$
0.220003 + 0.975499i $$0.429393\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ −77308.0 −3.80181
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −22516.0 −1.08105 −0.540527 0.841327i $$-0.681775\pi$$
−0.540527 + 0.841327i $$0.681775\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −27320.0 −1.30138 −0.650689 0.759344i $$-0.725520\pi$$
−0.650689 + 0.759344i $$0.725520\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −9650.00 −0.452520 −0.226260 0.974067i $$-0.572650\pi$$
−0.226260 + 0.974067i $$0.572650\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −39542.0 −1.83988 −0.919940 0.392060i $$-0.871763\pi$$
−0.919940 + 0.392060i $$0.871763\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 86328.0 3.92507
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 43056.0 1.92807
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −41954.0 −1.86460 −0.932300 0.361685i $$-0.882202\pi$$
−0.932300 + 0.361685i $$0.882202\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 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
$$809$$ −39704.0 −1.72549 −0.862743 0.505643i $$-0.831255\pi$$
−0.862743 + 0.505643i $$0.831255\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1850.00 0.0786424 0.0393212 0.999227i $$-0.487480\pi$$
0.0393212 + 0.999227i $$0.487480\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 41740.0 1.74872 0.874361 0.485276i $$-0.161281\pi$$
0.874361 + 0.485276i $$0.161281\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −35672.0 −1.48375
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −7489.00 −0.307065
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 137874. 5.61303
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ −45468.0 −1.82508 −0.912541 0.408986i $$-0.865883\pi$$
−0.912541 + 0.408986i $$0.865883\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 20056.0 0.799416 0.399708 0.916642i $$-0.369111\pi$$
0.399708 + 0.916642i $$0.369111\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ −89804.0 −3.52997
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 29844.0 1.14910 0.574550 0.818470i $$-0.305177\pi$$
0.574550 + 0.818470i $$0.305177\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 51808.0 1.98122 0.990611 0.136714i $$-0.0436541\pi$$
0.990611 + 0.136714i $$0.0436541\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −53872.0 −1.99194
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 62920.0 2.31108
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −142164. −5.05332
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 47480.0 1.67682 0.838411 0.545038i $$-0.183485\pi$$
0.838411 + 0.545038i $$0.183485\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 51946.0 1.81110 0.905551 0.424238i $$-0.139458\pi$$
0.905551 + 0.424238i $$0.139458\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −31378.0 −1.08703 −0.543514 0.839400i $$-0.682907\pi$$
−0.543514 + 0.839400i $$0.682907\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ −101016. −3.45534
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 15512.0 0.527264 0.263632 0.964623i $$-0.415079\pi$$
0.263632 + 0.964623i $$0.415079\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −29791.0 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −117964. −3.93512
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 22936.0 0.751062 0.375531 0.926810i $$-0.377460\pi$$
0.375531 + 0.926810i $$0.377460\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ −25828.0 −0.835481
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 34164.0 1.08524 0.542620 0.839978i $$-0.317432\pi$$
0.542620 + 0.839978i $$0.317432\pi$$
$$998$$ 0 0
$$999$$ 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 2304.4.a.p.1.1 1
3.2 odd 2 2304.4.a.b.1.1 1
4.3 odd 2 CM 2304.4.a.p.1.1 1
8.3 odd 2 2304.4.a.a.1.1 1
8.5 even 2 2304.4.a.a.1.1 1
12.11 even 2 2304.4.a.b.1.1 1
16.3 odd 4 1152.4.d.f.577.1 yes 2
16.5 even 4 1152.4.d.f.577.2 yes 2
16.11 odd 4 1152.4.d.f.577.2 yes 2
16.13 even 4 1152.4.d.f.577.1 yes 2
24.5 odd 2 2304.4.a.o.1.1 1
24.11 even 2 2304.4.a.o.1.1 1
48.5 odd 4 1152.4.d.c.577.1 2
48.11 even 4 1152.4.d.c.577.1 2
48.29 odd 4 1152.4.d.c.577.2 yes 2
48.35 even 4 1152.4.d.c.577.2 yes 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1152.4.d.c.577.1 2 48.5 odd 4
1152.4.d.c.577.1 2 48.11 even 4
1152.4.d.c.577.2 yes 2 48.29 odd 4
1152.4.d.c.577.2 yes 2 48.35 even 4
1152.4.d.f.577.1 yes 2 16.3 odd 4
1152.4.d.f.577.1 yes 2 16.13 even 4
1152.4.d.f.577.2 yes 2 16.5 even 4
1152.4.d.f.577.2 yes 2 16.11 odd 4
2304.4.a.a.1.1 1 8.3 odd 2
2304.4.a.a.1.1 1 8.5 even 2
2304.4.a.b.1.1 1 3.2 odd 2
2304.4.a.b.1.1 1 12.11 even 2
2304.4.a.o.1.1 1 24.5 odd 2
2304.4.a.o.1.1 1 24.11 even 2
2304.4.a.p.1.1 1 1.1 even 1 trivial
2304.4.a.p.1.1 1 4.3 odd 2 CM