LMFDB - Newform orbit 529.2.c.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,2,Mod(118,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("529.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	529.c (of order $11$, degree $10$, not 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:	no
Analytic conductor:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

Coefficients of the $q$-expansion are expressed in terms of a primitive root of unity $\zeta_{22}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	$ q + ( - \zeta_{22}^{8} - \zeta_{22}^{6} + \cdots - 1) q^{2}+ \cdots + ( - \zeta_{22}^{7} + \zeta_{22}^{6} + \cdots + 1) q^{9}+O(q^{10}) $ q + (-z^8 - z^6 - z^2 - 1) * q^2 + (z^7 + z^5 - z^4 - z^2) * q^3 + (2z^9 + 2z^7 + z^5 - z^4 + z - 1) * q^4 + (-z^8 + z^7 - z^4 + z^3 - 2z^2 + z - 1) q^5 + (z^9 - z^8 - z^6 + z^5 + z^4 + 2z^3 + z^2 + z - 1) q^6 + (-z^8 - z^6 + 2z^5 - z^4 - z^2) q^7 + (-2z^9 - z^7 + z^6 + 2z^4 + z^2 + z + 1) * q^8 + (-z^7 + z^6 + z^5 - z^2 - z + 1) * q^9	$ q + ( - \zeta_{22}^{8} - \zeta_{22}^{6} + \cdots - 1) q^{2}+ \cdots + ( - 2 \zeta_{22}^{9} + \cdots - 2 \zeta_{22}) q^{99}+O(q^{100}) $ q + (-z^8 - z^6 - z^2 - 1) * q^2 + (z^7 + z^5 - z^4 - z^2) * q^3 + (2z^9 + 2z^7 + z^5 - z^4 + z - 1) * q^4 + (-z^8 + z^7 - z^4 + z^3 - 2z^2 + z - 1) q^5 + (z^9 - z^8 - z^6 + z^5 + z^4 + 2z^3 + z^2 + z - 1) q^6 + (-z^8 - z^6 + 2z^5 - z^4 - z^2) q^7 + (-2z^9 - z^7 + z^6 + 2z^4 + z^2 + z + 1) * q^8 + (-z^7 + z^6 + z^5 - z^2 - z + 1) * q^9 + (z^9 + 2z^7 - 2z^6 + 2z^5 + z^3 + 2z - 2) * q^10 + (3z^7 + z^3 - z^2 + z - 1) q^11 + (-3z^9 + z^8 - z^7 + z^6 - 3z^5 - 4z^3 + 2z^2 - 2z + 4) q^12 + (z^9 - 2z^8 + z^7 + z^5 - 2z^4 + z^3) * q^13 + (3z^9 + z^7 - z^6 - z^4 + z^3 + z - 1) q^14 + (-2z^9 + z^8 - 2z^7 + 2z^6 - z^5 + 2z^4) * q^15 + (-3z^9 + 2z^8 - 3z^7 + z^6 - 3z^5 + z^4 - 3z^3 + 2z^2 - 3z) q^16 + (-2z^9 + 2z^8 + z^6 - z^5 + 2z^4 + 2z^3 + 2z^2 - z + 1) q^17 + (3z^9 - 2z^8 + 2z^7 - 3z^6 - z^4 + 3z^3 - z^2 + 3z - 1) * q^18 + (-2z^9 - 2z^8 - 2z^7 + 2z^5 - 2) * q^19 + (-4z^9 + 2z^8 - 2z^7 + z^6 - z^5 + z^4 - z^3 + 2z^2 - 2z + 4) q^20 + (-2z^8 + z^7 - 2z^6 + 4z^5 - 2z^4 + 4z^3 - 2z^2 + z - 2) * q^21 + (-4z^9 + z^8 - 3z^7 + 3z^4 - z^3 + 4z^2 + 1) * q^22 + (3z^9 - z^8 + z^7 - z^6 + z^5 - z^4 + z^3 - 3z^2 - 5) * q^24 + (-z^8 + 2z^7 - z^6 - z^5 - z^4 - z^3 - z^2 + 2z - 1) * q^25 + (z^9 - 2z^8 + 2z^7 - z^6 + z^3 - 2z^2 + 2z - 1) * q^26 + (-z^9 - 2z^8 - z^7 - z^5 - z^3 + z^2 + 1) q^27 + (-3z^9 - z^8 + z^7 + 3z^6 + 2z^4 - 2z^3 + 3z^2 - 2z + 2) * q^28 + (z^9 - z^8 + 2z^5 - 4z^4 - 4z^2 + 2z) * q^29 + (z^9 - 3z^6 - z^5 - 3z^4 + z) * q^30 + (2z^9 - 2z^8 + 2z^5 - 2z^4 - z^2 - 1) * q^31 + (3z^9 + 2z^7 - 2z^6 + z^5 - 4z^4 + 4z^3 - z^2 + 2z - 2) * q^32 + (-3z^9 + z^8 - 2z^7 + z^6 - 2z^5 + z^4 - 3z^3 - 2z + 2) q^33 + (-5z^9 - 4z^7 - 5z^5 - 4z^3 + 2z^2 - 2z + 4) * q^34 + (-z^9 + 2z^8 - 2z^7 + 2z^6 - z^5 + 2z^3 - 2) * q^35 + (-3z^9 - z^8 + z^7 + 2z^6 + z^5 - z^4 - 3z^3 - z + 1) q^36 + (-3z^9 - z^7 + z^6 - 2z^5 + 4z^4 - 4z^3 + 2z^2 - z + 1) q^37 + (6z^9 + 2z^8 + 2z^7 - 2z^6 - 2z^5 - 6z^4 + 2z) q^38 + (-z^8 + 2z^7 - 2z^6 + 2z^5 - 2z^4 + 2z^3 - z^2) q^39 + (-3z^6 - z^5 - 3z^3 - z - 3) * q^40 + (z^9 - 3z^8 + 3z^7 - z^6 + z^2) * q^41 + (2z^8 - 4z^5 - z^4 - 3z^3 + 3z^2 + z + 4) * q^42 + (-2z^7 - z^6 + z^5 - z^4 + z^3 + 2z^2) * q^43 + (2z^8 - 3z^7 - 2z^6 - 4z^5 - 2z^4 - 4z^3 - 2z^2 - 3z + 2) * q^44 + (z^9 - 3z^8 + 2z^6 - 2z^5 + 3z^3 - z^2 - 1) * q^45 + (-z^9 + 2z^8 - 2z^7 - z^6 + z^5 + 2z^4 - 2z^3 + z^2 - 1) * q^47 + (z^8 - z^7 + 3z^6 + 5z^4 + 3z^2 - z + 1) q^48 + (-3z^9 + 2z^8 - 3z^7 + z^6 - z^3 + 3z^2 - 2z + 3) q^49 + (z^8 + 4z^5 + z^4 - z - 4) q^50 + (3z^9 - 3z^6 - 3z^4 + z^3 - 4z^2 + z - 3) * q^51 + (-2z^9 + 2z^8 + z^6 - 3z^5 + 3z^4 - 2z^3 + 3z^2 - 3z + 1) q^52 + (4z^9 + 3z^8 - z^7 + 2z^6 + 2z^4 - z^3 + 3z^2 + 4z) * q^53 + (4z^9 - z^8 + 3z^7 - 3z^6 + z^5 - 4z^4 - 5z^2 + z - 5) q^54 + (-3z^9 - 3z^6 + z^5 + 3z^4 - 3z^3 - z^2 + 3z) q^55 + (-z^8 - 3z^7 - 3z^5 - z^4 + z - 1) * q^56 + (4z^9 - 4z^8 - 4z^6 + 4z^5 + 8z^3 - 2z^2 + 2z - 8) q^57 + (6z^9 - 4z^8 + 5z^7 - 4z^6 + 6z^5 + 6z^3 - 3z^2 + 3z - 6) * q^58 + (2z^9 + 3z^8 - 3z^6 + 3z^4 + 2z^3) q^59 + (z^9 + 3z^7 + 6z^5 - 3z^4 + 3z^3 - 6z^2 - 3) q^60 + (-6z^9 + z^8 - 3z^7 + 3z^6 - z^5 + 6z^4 + 4z^2 - 2z + 4) * q^61 + (3z^9 - z^8 + 3z^7 + z^5 + 3z^3 - z^2 + 3z) * q^62 + (3z^9 - 3z^8 - 4z^6 + 5z^5 - 3z^4 + 4z^3 - 3z^2 + 5z - 4) * q^63 + (-4z^9 + 4z^8 - 4z^7 + 4z^6 + 3z^4 - 5z^3 - z^2 - 5z + 3) q^64 + (z^9 - z^8 + z^7 - z^5 - z^4 + 5z^3 - 5z^2 + z + 1) * q^65 + (8z^9 - 2z^8 + 4z^7 - 5z^6 + 4z^5 - 4z^4 + 5z^3 - 4z^2 + 2z - 8) q^66 + (-z^8 - 2z^7 + 6z^6 - z^5 + 5z^4 - z^3 + 6z^2 - 2z - 1) q^67 + (11z^9 - 2z^8 + 5z^7 - 7z^6 + 7z^5 - 5z^4 + 2z^3 - 11z^2 - 8) * q^68 + (-z^9 + z^7 + z^6 - z^5 - z^4 + z^2 + 4) * q^70 + (z^8 - 2z^6 + 2z^5 - 2z^4 + 2z^3 - 2z^2 + 1) q^71 + (4z^9 - 4z^8 + 3z^7 - 3z^6 + z^5 - z^4 + 3z^3 - 3z^2 + 4z - 4) q^72 + (-z^9 - 3z^8 - z^7 - 2z^5 + 2z^4 + 2z^3 - 2z^2 - 2z + 2) * q^73 + (3z^9 + 2z^8 - 2z^7 - 3z^6 - 4z^4 - 4) q^74 + (-3z^9 + 3z^8 + 4z^6 - 2z^5 + 3z^4 - 4z^3 + 3z^2 - 2z + 4) * q^75 + (-6z^9 + 2z^7 + 6z^6 + 4z^5 + 6z^4 + 2z^3 - 6z) q^76 + (-4z^9 + 3z^8 - 3z^7 + 3z^6 - 3z^5 + 4z^4 + 3z^2 - 5z + 3) * q^77 + (-z^5 + z^4 - z^3 + z^2) * q^78 + (3z^9 - 6z^8 - 4z^6 - 6z^4 + 3z^3 - 2z + 2) * q^79 + (4z^9 + 2z^8 - 2z^7 + 2z^6 + 4z^5 - z^3 + 4z^2 - 4z + 1) q^80 + (3z^9 + 2z^8 + z^7 + 2z^6 + 3z^5 - 4z^3 + 3z^2 - 3z + 4) q^81 + (-2z^9 + z^8 - z^7 - z^5 + z^4 - 2z^3 + z - 1) * q^82 + (4z^9 + 2z^7 - 3z^6 - z^5 - 3z^4 + 3z^3 + z^2 + 3z - 2) * q^83 + (-5z^8 + 3z^7 - 3z^6 + 5z^5 - 3z^2 - 6z - 3) * q^84 + (2z^9 - 2z^8 - 3z^7 - z^6 - z^5 - z^4 - 3z^3 - 2z^2 + 2z) * q^85 + (3z^6 - 3z^5 - 2z^4 - 3z^3 - 2z^2 - 3z + 3) * q^86 + (-7z^9 + 3z^8 - 3z^7 + 7z^6 + 2z^4 - z^2 + 2) q^87 + (4z^9 + 4z^8 + 4z^7 + 6z^5 + z^4 + z^3 - z^2 - z - 6) * q^88 + (-4z^9 - 3z^8 - z^7 + 8z^6 - 5z^5 + 5z^4 - 8z^3 + z^2 + 3z + 4) q^89 + (-z^8 + 6z^7 - 4z^6 - 2z^4 - 4z^2 + 6z - 1) q^90 + (-z^9 - 2z^8 + 4z^7 - 3z^6 + 3z^5 - 4z^4 + 2z^3 + z^2 - 2) * q^91 + (-z^9 - 2z^8 - z^6 + z^5 + 2z^3 + z^2) * q^93 + (4z^8 - 4z^7 + 4z^6 - 2z^5 - z^4 - 2z^3 + 4z^2 - 4z + 4) q^94 + (2z^9 + 4z^8 - 4z^7 - 2z^5 + 2z^4 + 4z^2 - 4z - 2) q^95 + (-z^9 + 5z^8 - z^7 - 4z^5 - 4z^4 + 4z + 4) * q^96 + (-2z^9 + 5z^8 - 5z^7 + 2z^6 + 7z^4 + 6z^2 + 7) * q^97 + (4z^9 - 4z^8 - 2z^6 - 2z^5 - 4z^4 + z^3 - 4z^2 - 2z - 2) q^98 + (-2z^9 - 3z^8 + 3z^7 + z^6 - 3z^5 + z^4 + 3z^3 - 3z^2 - 2z) q^99
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 7 q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} + 6 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) $ 10 * q - 7 * q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 + 6 * q^7 + 4 * q^8 + 9 * q^9	\( 10 q - 7 q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} + 6 q^{7} + 4 q^{8} + 9 q^{9} - 10 q^{10} - 4 q^{11} + 23 q^{12} + 8 q^{13} - 2 q^{14} - 10 q^{15} - 21 q^{16} + q^{17} + 8 q^{18} - 20 q^{19} + 24 q^{20} - 2 q^{21} - 6 q^{22} - 38 q^{24} - 4 q^{25} + q^{26} + 7 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} - q^{31} - q^{32} + 5 q^{33} + 18 q^{34} - 26 q^{35} + 5 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 32 q^{40} + 7 q^{41} + 30 q^{42} + 10 q^{44} - 6 q^{45} - 18 q^{47} - 4 q^{48} + 15 q^{49} - 39 q^{50} - 15 q^{51} - 9 q^{52} - 4 q^{53} - 28 q^{54} - q^{55} - 13 q^{56} - 52 q^{57} - 23 q^{58} + q^{59} - 8 q^{60} + 14 q^{61} + 15 q^{62} - 10 q^{63} + 2 q^{64} + 24 q^{65} - 42 q^{66} - 32 q^{67} - 30 q^{68} + 38 q^{70} + 19 q^{71} - 14 q^{72} + 19 q^{73} - 34 q^{74} + 16 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} + 40 q^{79} + 3 q^{80} + 33 q^{81} - 17 q^{82} - 4 q^{83} - 17 q^{84} + 3 q^{85} + 22 q^{86} - q^{87} - 50 q^{88} + 14 q^{89} + 13 q^{90} - 4 q^{91} + 4 q^{93} + 17 q^{94} - 38 q^{95} + 37 q^{96} + 43 q^{97} - 5 q^{98} + 3 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 + 6 * q^7 + 4 * q^8 + 9 * q^9 - 10 * q^10 - 4 * q^11 + 23 * q^12 + 8 * q^13 - 2 * q^14 - 10 * q^15 - 21 * q^16 + q^17 + 8 * q^18 - 20 * q^19 + 24 * q^20 - 2 * q^21 - 6 * q^22 - 38 * q^24 - 4 * q^25 + q^26 + 7 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 - q^31 - q^32 + 5 * q^33 + 18 * q^34 - 26 * q^35 + 5 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 32 * q^40 + 7 * q^41 + 30 * q^42 + 10 * q^44 - 6 * q^45 - 18 * q^47 - 4 * q^48 + 15 * q^49 - 39 * q^50 - 15 * q^51 - 9 * q^52 - 4 * q^53 - 28 * q^54 - q^55 - 13 * q^56 - 52 * q^57 - 23 * q^58 + q^59 - 8 * q^60 + 14 * q^61 + 15 * q^62 - 10 * q^63 + 2 * q^64 + 24 * q^65 - 42 * q^66 - 32 * q^67 - 30 * q^68 + 38 * q^70 + 19 * q^71 - 14 * q^72 + 19 * q^73 - 34 * q^74 + 16 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 + 40 * q^79 + 3 * q^80 + 33 * q^81 - 17 * q^82 - 4 * q^83 - 17 * q^84 + 3 * q^85 + 22 * q^86 - q^87 - 50 * q^88 + 14 * q^89 + 13 * q^90 - 4 * q^91 + 4 * q^93 + 17 * q^94 - 38 * q^95 + 37 * q^96 + 43 * q^97 - 5 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$\zeta_{22}^{4}$

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

118.1

−0.415415	−	0.909632i
0.654861	−	0.755750i
−0.841254	−	0.540641i
0.142315	−	0.989821i
−0.841254	+	0.540641i
0.142315	+	0.989821i
−0.415415	+	0.909632i
0.959493	−	0.281733i
0.959493	+	0.281733i
0.654861	+	0.755750i

−0.226900

−

1.57812i

0.0982369

−

0.215109i

−0.520003

0.152687i

2.09792

−

2.42113i

−0.361758

−

0.106222i

−0.767092

0.492980i

−0.965688

−

2.11456i

1.92796

2.22499i

−4.29686

−

2.76142i

170.1

−2.11435

0.620830i

1.64589

1.89945i

2.40255

−

1.54403i

0.175969

1.22389i

−4.65922

−

2.99430i

−0.985691

2.15836i

−1.23515

1.42544i

−0.472039

3.28310i

−1.13189

−

2.47850i

177.1

−0.313607

0.361922i

1.85380

−

1.19136i

0.251992

1.75264i

−1.07773

−

2.35990i

−0.150184

1.04455i

3.26024

−

0.957293i

−1.51908

−

0.976256i

0.770978

−

1.68821i

1.19209

0.350028i

255.1

0.198939

0.127850i

−0.0681534

−

0.474017i

−0.807599

−

1.76840i

−1.45204

−

0.426356i

0.0470448

−

0.103014i

1.66741

−

1.92429i

0.132736

−

0.923198i

2.65843

−

0.780586i

−0.234356

−

0.270462i

266.1

−0.313607

−

0.361922i

1.85380

1.19136i

0.251992

−

1.75264i

−1.07773

2.35990i

−0.150184

−

1.04455i

3.26024

0.957293i

−1.51908

0.976256i

0.770978

1.68821i

1.19209

−

0.350028i

334.1

0.198939

−

0.127850i

−0.0681534

0.474017i

−0.807599

1.76840i

−1.45204

0.426356i

0.0470448

0.103014i

1.66741

1.92429i

0.132736

0.923198i

2.65843

0.780586i

−0.234356

0.270462i

399.1

−0.226900

1.57812i

0.0982369

0.215109i

−0.520003

−

0.152687i

2.09792

2.42113i

−0.361758

0.106222i

−0.767092

−

0.492980i

−0.965688

2.11456i

1.92796

−

2.22499i

−4.29686

2.76142i

466.1

−1.04408

2.28621i

−1.52977

−

0.449181i

−2.82694

−

3.26247i

−1.24412

0.799549i

2.62412

−

3.02840i

−0.174863

1.21620i

5.58718

−

1.64055i

−0.385331

−

0.247638i

−0.528978

−

3.67912i

487.1

−1.04408

−

2.28621i

−1.52977

0.449181i

−2.82694

3.26247i

−1.24412

−

0.799549i

2.62412

3.02840i

−0.174863

−

1.21620i

5.58718

1.64055i

−0.385331

0.247638i

−0.528978

3.67912i

501.1

−2.11435

−

0.620830i

1.64589

−

1.89945i

2.40255

1.54403i

0.175969

−

1.22389i

−4.65922

2.99430i

−0.985691

−

2.15836i

−1.23515

−

1.42544i

−0.472039

−

3.28310i

−1.13189

2.47850i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.c	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	529.2.c.b		10
23.b	odd	2	1		529.2.c.c		10
23.c	even	11	2		23.2.c.a	✓	10
23.c	even	11	1		529.2.a.i		5
23.c	even	11	1	inner	529.2.c.b		10
23.c	even	11	2		529.2.c.d		10
23.c	even	11	2		529.2.c.g		10
23.c	even	11	2		529.2.c.i		10
23.d	odd	22	1		529.2.a.j		5
23.d	odd	22	2		529.2.c.a		10
23.d	odd	22	1		529.2.c.c		10
23.d	odd	22	2		529.2.c.e		10
23.d	odd	22	2		529.2.c.f		10
23.d	odd	22	2		529.2.c.h		10
69.g	even	22	1		4761.2.a.bn		5
69.h	odd	22	2		207.2.i.c		10
69.h	odd	22	1		4761.2.a.bo		5
92.g	odd	22	2		368.2.m.c		10
92.g	odd	22	1		8464.2.a.bs		5
92.h	even	22	1		8464.2.a.bt		5
115.j	even	22	2		575.2.k.b		10
115.k	odd	44	4		575.2.p.b		20

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.2.c.a	✓	10	23.c	even	11	2
207.2.i.c		10	69.h	odd	22	2
368.2.m.c		10	92.g	odd	22	2
529.2.a.i		5	23.c	even	11	1
529.2.a.j		5	23.d	odd	22	1
529.2.c.a		10	23.d	odd	22	2
529.2.c.b		10	1.a	even	1	1	trivial
529.2.c.b		10	23.c	even	11	1	inner
529.2.c.c		10	23.b	odd	2	1
529.2.c.c		10	23.d	odd	22	1
529.2.c.d		10	23.c	even	11	2
529.2.c.e		10	23.d	odd	22	2
529.2.c.f		10	23.d	odd	22	2
529.2.c.g		10	23.c	even	11	2
529.2.c.h		10	23.d	odd	22	2
529.2.c.i		10	23.c	even	11	2
575.2.k.b		10	115.j	even	22	2
575.2.p.b		20	115.k	odd	44	4
4761.2.a.bn		5	69.g	even	22	1
4761.2.a.bo		5	69.h	odd	22	1
8464.2.a.bs		5	92.g	odd	22	1
8464.2.a.bt		5	92.h	even	22	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(529, [\chi])$:

$ T_{2}^{10} + 7T_{2}^{9} + 27T_{2}^{8} + 68T_{2}^{7} + 113T_{2}^{6} + 131T_{2}^{5} + 103T_{2}^{4} + 17T_{2}^{3} - 2T_{2}^{2} - 3T_{2} + 1 $

$ T_{5}^{10} + 3 T_{5}^{9} + 9 T_{5}^{8} + 27 T_{5}^{7} + 114 T_{5}^{6} + 386 T_{5}^{5} + 806 T_{5}^{4} + \cdots + 529 $

$ T_{7}^{10} - 6 T_{7}^{9} + 14 T_{7}^{8} - 29 T_{7}^{7} + 86 T_{7}^{6} - 153 T_{7}^{5} + 126 T_{7}^{4} + \cdots + 529 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T^{10} + 7 T^{9} + \cdots + 1 $ T^10 + 7T^9 + 27T^8 + 68T^7 + 113T^6 + 131T^5 + 103T^4 + 17T^3 - 2T^2 - 3*T + 1
$3$	$ T^{10} - 4 T^{9} + \cdots + 1 $ T^10 - 4T^9 + 5T^8 + 13T^7 - 30T^6 - T^5 + 70T^4 - 5T^3 + 20T^2 - 3T + 1
$5$	$ T^{10} + 3 T^{9} + \cdots + 529 $ T^10 + 3T^9 + 9T^8 + 27T^7 + 114T^6 + 386T^5 + 806T^4 + 1120T^3 + 1248T^2 + 1104*T + 529
$7$	$ T^{10} - 6 T^{9} + \cdots + 529 $ T^10 - 6T^9 + 14T^8 - 29T^7 + 86T^6 - 153T^5 + 126T^4 + 201T^3 + 587T^2 + 713*T + 529
$11$	$ T^{10} + 4 T^{9} + \cdots + 529 $ T^10 + 4T^9 + 27T^8 + 75T^7 + 190T^6 - 219T^5 - 1173T^4 - 3735T^3 + 9040T^2 + 2852*T + 529
$13$	$ T^{10} - 8 T^{9} + \cdots + 1 $ T^10 - 8T^9 + 20T^8 - 17T^7 + 180T^6 - 989T^5 + 1598T^4 - 343T^3 + 93T^2 - 7*T + 1
$17$	$ T^{10} - T^{9} + \cdots + 529 $ T^10 - T^9 + 34T^8 - 67T^7 + 1354T^6 + 2155T^5 + 5061T^4 + 8733T^3 + 8955T^2 - 4577T + 529
$19$	$ T^{10} + 20 T^{9} + \cdots + 541696 $ T^10 + 20T^9 + 180T^8 + 872T^7 + 3008T^6 + 8416T^5 + 28224T^4 + 106880T^3 + 256512T^2 + 376832*T + 541696
$23$	$ T^{10} $ T^10
$29$	$ T^{10} - 14 T^{9} + \cdots + 4932841 $ T^10 - 14T^9 + 152T^8 - 1028T^7 + 5537T^6 - 23805T^5 + 103678T^4 - 469632T^3 + 2050064T^2 - 5097195*T + 4932841
$31$	$ T^{10} + T^{9} + \cdots + 17161 $ T^10 + T^9 + 23T^8 + 89T^7 + 122T^6 + 760T^5 + 2036T^4 - 604T^3 - 2507T^2 - 131T + 17161
$37$	$ T^{10} + 8 T^{9} + \cdots + 529 $ T^10 + 8T^9 + 75T^8 + 105T^7 + 598T^6 - 3147T^5 + 19869T^4 - 3925T^3 + 366514T^2 + 26726*T + 529
$41$	$ T^{10} - 7 T^{9} + \cdots + 1849 $ T^10 - 7T^9 + 60T^8 + 75T^7 - 690T^6 + 2289T^5 + 7022T^4 - 14031T^3 + 9557T^2 - 1548*T + 1849
$43$	$ T^{10} + 11 T^{8} + \cdots + 64009 $ T^10 + 11T^8 - 154T^7 + 297T^6 - 627T^5 + 7986T^4 - 28314T^3 + 40051T^2 - 36179T + 64009
$47$	$ (T^{5} + 9 T^{4} - 5 T^{3} + \cdots + 1)^{2} $ (T^5 + 9T^4 - 5T^3 - 97T^2 - 106T + 1)^2
$53$	$ T^{10} + \cdots + 517426009 $ T^10 + 4T^9 + 93T^8 + 1626T^7 + 6735T^6 + 77661T^5 + 869862T^4 + 1581112T^3 + 17636331T^2 + 159570205*T + 517426009
$59$	$ T^{10} - T^{9} + \cdots + 4489 $ T^10 - T^9 + 67T^8 + 296T^7 + 7558T^6 + 43867T^5 + 230297T^4 + 726934T^3 + 1261107T^2 + 142174T + 4489
$61$	$ T^{10} - 14 T^{9} + \cdots + 529 $ T^10 - 14T^9 - 35T^8 + 72T^7 + 10443T^6 + 28247T^5 + 172340T^4 + 199234T^3 + 282265T^2 + 20401*T + 529
$67$	$ T^{10} + \cdots + 1113757129 $ T^10 + 32T^9 + 562T^8 + 6764T^7 + 72755T^6 + 716836T^5 + 5485624T^4 + 31047598T^3 + 143629619T^2 + 534535341*T + 1113757129
$71$	$ T^{10} - 19 T^{9} + \cdots + 529 $ T^10 - 19T^9 + 185T^8 - 897T^7 + 2358T^6 - 3222T^5 + 4040T^4 - 2840T^3 + 1457T^2 - 1173*T + 529
$73$	$ T^{10} - 19 T^{9} + \cdots + 982081 $ T^10 - 19T^9 + 97T^8 + 126T^7 - 1184T^6 - 11725T^5 + 197761T^4 - 854680T^3 + 2441367T^2 - 780908*T + 982081
$79$	$ T^{10} + \cdots + 517426009 $ T^10 - 40T^9 + 742T^8 - 8670T^7 + 74418T^6 - 431232T^5 + 1533250T^4 - 9461073T^3 + 59672787T^2 + 194100151*T + 517426009
$83$	$ T^{10} + 4 T^{9} + \cdots + 529 $ T^10 + 4T^9 + 159T^8 + 1219T^7 + 3413T^6 + 3620T^5 + 972T^4 + 1160T^3 + 4310T^2 + 1334*T + 529
$89$	$ T^{10} + \cdots + 78310985281 $ T^10 - 14T^9 + 185T^8 - 423T^7 + 26558T^6 - 613801T^5 + 14234861T^4 - 226561707T^3 + 2553269284T^2 - 20132880904*T + 78310985281
$97$	$ T^{10} - 43 T^{9} + \cdots + 2374681 $ T^10 - 43T^9 + 716T^8 - 4333T^7 + 5402T^6 - 83313T^5 + 745405T^4 + 1316019T^3 + 15427259T^2 + 5120743*T + 2374681
show more
show less

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\( q + ( - \zeta_{22}^{8} - \zeta_{22}^{6} + \cdots - 1) q^{2}+ \cdots + ( - \zeta_{22}^{7} + \zeta_{22}^{6} + \cdots + 1) q^{9}+O(q^{10}) \) q + (-z^8 - z^6 - z^2 - 1) * q^2 + (z^7 + z^5 - z^4 - z^2) * q^3 + (2z^9 + 2z^7 + z^5 - z^4 + z - 1) * q^4 + (-z^8 + z^7 - z^4 + z^3 - 2z^2 + z - 1) q^5 + (z^9 - z^8 - z^6 + z^5 + z^4 + 2z^3 + z^2 + z - 1) q^6 + (-z^8 - z^6 + 2z^5 - z^4 - z^2) q^7 + (-2z^9 - z^7 + z^6 + 2z^4 + z^2 + z + 1) * q^8 + (-z^7 + z^6 + z^5 - z^2 - z + 1) * q^9	\( q + ( - \zeta_{22}^{8} - \zeta_{22}^{6} + \cdots - 1) q^{2}+ \cdots + ( - 2 \zeta_{22}^{9} + \cdots - 2 \zeta_{22}) q^{99}+O(q^{100}) \) q + (-z^8 - z^6 - z^2 - 1) * q^2 + (z^7 + z^5 - z^4 - z^2) * q^3 + (2z^9 + 2z^7 + z^5 - z^4 + z - 1) * q^4 + (-z^8 + z^7 - z^4 + z^3 - 2z^2 + z - 1) q^5 + (z^9 - z^8 - z^6 + z^5 + z^4 + 2z^3 + z^2 + z - 1) q^6 + (-z^8 - z^6 + 2z^5 - z^4 - z^2) q^7 + (-2z^9 - z^7 + z^6 + 2z^4 + z^2 + z + 1) * q^8 + (-z^7 + z^6 + z^5 - z^2 - z + 1) * q^9 + (z^9 + 2z^7 - 2z^6 + 2z^5 + z^3 + 2z - 2) * q^10 + (3z^7 + z^3 - z^2 + z - 1) q^11 + (-3z^9 + z^8 - z^7 + z^6 - 3z^5 - 4z^3 + 2z^2 - 2z + 4) q^12 + (z^9 - 2z^8 + z^7 + z^5 - 2z^4 + z^3) * q^13 + (3z^9 + z^7 - z^6 - z^4 + z^3 + z - 1) q^14 + (-2z^9 + z^8 - 2z^7 + 2z^6 - z^5 + 2z^4) * q^15 + (-3z^9 + 2z^8 - 3z^7 + z^6 - 3z^5 + z^4 - 3z^3 + 2z^2 - 3z) q^16 + (-2z^9 + 2z^8 + z^6 - z^5 + 2z^4 + 2z^3 + 2z^2 - z + 1) q^17 + (3z^9 - 2z^8 + 2z^7 - 3z^6 - z^4 + 3z^3 - z^2 + 3z - 1) * q^18 + (-2z^9 - 2z^8 - 2z^7 + 2z^5 - 2) * q^19 + (-4z^9 + 2z^8 - 2z^7 + z^6 - z^5 + z^4 - z^3 + 2z^2 - 2z + 4) q^20 + (-2z^8 + z^7 - 2z^6 + 4z^5 - 2z^4 + 4z^3 - 2z^2 + z - 2) * q^21 + (-4z^9 + z^8 - 3z^7 + 3z^4 - z^3 + 4z^2 + 1) * q^22 + (3z^9 - z^8 + z^7 - z^6 + z^5 - z^4 + z^3 - 3z^2 - 5) * q^24 + (-z^8 + 2z^7 - z^6 - z^5 - z^4 - z^3 - z^2 + 2z - 1) * q^25 + (z^9 - 2z^8 + 2z^7 - z^6 + z^3 - 2z^2 + 2z - 1) * q^26 + (-z^9 - 2z^8 - z^7 - z^5 - z^3 + z^2 + 1) q^27 + (-3z^9 - z^8 + z^7 + 3z^6 + 2z^4 - 2z^3 + 3z^2 - 2z + 2) * q^28 + (z^9 - z^8 + 2z^5 - 4z^4 - 4z^2 + 2z) * q^29 + (z^9 - 3z^6 - z^5 - 3z^4 + z) * q^30 + (2z^9 - 2z^8 + 2z^5 - 2z^4 - z^2 - 1) * q^31 + (3z^9 + 2z^7 - 2z^6 + z^5 - 4z^4 + 4z^3 - z^2 + 2z - 2) * q^32 + (-3z^9 + z^8 - 2z^7 + z^6 - 2z^5 + z^4 - 3z^3 - 2z + 2) q^33 + (-5z^9 - 4z^7 - 5z^5 - 4z^3 + 2z^2 - 2z + 4) * q^34 + (-z^9 + 2z^8 - 2z^7 + 2z^6 - z^5 + 2z^3 - 2) * q^35 + (-3z^9 - z^8 + z^7 + 2z^6 + z^5 - z^4 - 3z^3 - z + 1) q^36 + (-3z^9 - z^7 + z^6 - 2z^5 + 4z^4 - 4z^3 + 2z^2 - z + 1) q^37 + (6z^9 + 2z^8 + 2z^7 - 2z^6 - 2z^5 - 6z^4 + 2z) q^38 + (-z^8 + 2z^7 - 2z^6 + 2z^5 - 2z^4 + 2z^3 - z^2) q^39 + (-3z^6 - z^5 - 3z^3 - z - 3) * q^40 + (z^9 - 3z^8 + 3z^7 - z^6 + z^2) * q^41 + (2z^8 - 4z^5 - z^4 - 3z^3 + 3z^2 + z + 4) * q^42 + (-2z^7 - z^6 + z^5 - z^4 + z^3 + 2z^2) * q^43 + (2z^8 - 3z^7 - 2z^6 - 4z^5 - 2z^4 - 4z^3 - 2z^2 - 3z + 2) * q^44 + (z^9 - 3z^8 + 2z^6 - 2z^5 + 3z^3 - z^2 - 1) * q^45 + (-z^9 + 2z^8 - 2z^7 - z^6 + z^5 + 2z^4 - 2z^3 + z^2 - 1) * q^47 + (z^8 - z^7 + 3z^6 + 5z^4 + 3z^2 - z + 1) q^48 + (-3z^9 + 2z^8 - 3z^7 + z^6 - z^3 + 3z^2 - 2z + 3) q^49 + (z^8 + 4z^5 + z^4 - z - 4) q^50 + (3z^9 - 3z^6 - 3z^4 + z^3 - 4z^2 + z - 3) * q^51 + (-2z^9 + 2z^8 + z^6 - 3z^5 + 3z^4 - 2z^3 + 3z^2 - 3z + 1) q^52 + (4z^9 + 3z^8 - z^7 + 2z^6 + 2z^4 - z^3 + 3z^2 + 4z) * q^53 + (4z^9 - z^8 + 3z^7 - 3z^6 + z^5 - 4z^4 - 5z^2 + z - 5) q^54 + (-3z^9 - 3z^6 + z^5 + 3z^4 - 3z^3 - z^2 + 3z) q^55 + (-z^8 - 3z^7 - 3z^5 - z^4 + z - 1) * q^56 + (4z^9 - 4z^8 - 4z^6 + 4z^5 + 8z^3 - 2z^2 + 2z - 8) q^57 + (6z^9 - 4z^8 + 5z^7 - 4z^6 + 6z^5 + 6z^3 - 3z^2 + 3z - 6) * q^58 + (2z^9 + 3z^8 - 3z^6 + 3z^4 + 2z^3) q^59 + (z^9 + 3z^7 + 6z^5 - 3z^4 + 3z^3 - 6z^2 - 3) q^60 + (-6z^9 + z^8 - 3z^7 + 3z^6 - z^5 + 6z^4 + 4z^2 - 2z + 4) * q^61 + (3z^9 - z^8 + 3z^7 + z^5 + 3z^3 - z^2 + 3z) * q^62 + (3z^9 - 3z^8 - 4z^6 + 5z^5 - 3z^4 + 4z^3 - 3z^2 + 5z - 4) * q^63 + (-4z^9 + 4z^8 - 4z^7 + 4z^6 + 3z^4 - 5z^3 - z^2 - 5z + 3) q^64 + (z^9 - z^8 + z^7 - z^5 - z^4 + 5z^3 - 5z^2 + z + 1) * q^65 + (8z^9 - 2z^8 + 4z^7 - 5z^6 + 4z^5 - 4z^4 + 5z^3 - 4z^2 + 2z - 8) q^66 + (-z^8 - 2z^7 + 6z^6 - z^5 + 5z^4 - z^3 + 6z^2 - 2z - 1) q^67 + (11z^9 - 2z^8 + 5z^7 - 7z^6 + 7z^5 - 5z^4 + 2z^3 - 11z^2 - 8) * q^68 + (-z^9 + z^7 + z^6 - z^5 - z^4 + z^2 + 4) * q^70 + (z^8 - 2z^6 + 2z^5 - 2z^4 + 2z^3 - 2z^2 + 1) q^71 + (4z^9 - 4z^8 + 3z^7 - 3z^6 + z^5 - z^4 + 3z^3 - 3z^2 + 4z - 4) q^72 + (-z^9 - 3z^8 - z^7 - 2z^5 + 2z^4 + 2z^3 - 2z^2 - 2z + 2) * q^73 + (3z^9 + 2z^8 - 2z^7 - 3z^6 - 4z^4 - 4) q^74 + (-3z^9 + 3z^8 + 4z^6 - 2z^5 + 3z^4 - 4z^3 + 3z^2 - 2z + 4) * q^75 + (-6z^9 + 2z^7 + 6z^6 + 4z^5 + 6z^4 + 2z^3 - 6z) q^76 + (-4z^9 + 3z^8 - 3z^7 + 3z^6 - 3z^5 + 4z^4 + 3z^2 - 5z + 3) * q^77 + (-z^5 + z^4 - z^3 + z^2) * q^78 + (3z^9 - 6z^8 - 4z^6 - 6z^4 + 3z^3 - 2z + 2) * q^79 + (4z^9 + 2z^8 - 2z^7 + 2z^6 + 4z^5 - z^3 + 4z^2 - 4z + 1) q^80 + (3z^9 + 2z^8 + z^7 + 2z^6 + 3z^5 - 4z^3 + 3z^2 - 3z + 4) q^81 + (-2z^9 + z^8 - z^7 - z^5 + z^4 - 2z^3 + z - 1) * q^82 + (4z^9 + 2z^7 - 3z^6 - z^5 - 3z^4 + 3z^3 + z^2 + 3z - 2) * q^83 + (-5z^8 + 3z^7 - 3z^6 + 5z^5 - 3z^2 - 6z - 3) * q^84 + (2z^9 - 2z^8 - 3z^7 - z^6 - z^5 - z^4 - 3z^3 - 2z^2 + 2z) * q^85 + (3z^6 - 3z^5 - 2z^4 - 3z^3 - 2z^2 - 3z + 3) * q^86 + (-7z^9 + 3z^8 - 3z^7 + 7z^6 + 2z^4 - z^2 + 2) q^87 + (4z^9 + 4z^8 + 4z^7 + 6z^5 + z^4 + z^3 - z^2 - z - 6) * q^88 + (-4z^9 - 3z^8 - z^7 + 8z^6 - 5z^5 + 5z^4 - 8z^3 + z^2 + 3z + 4) q^89 + (-z^8 + 6z^7 - 4z^6 - 2z^4 - 4z^2 + 6z - 1) q^90 + (-z^9 - 2z^8 + 4z^7 - 3z^6 + 3z^5 - 4z^4 + 2z^3 + z^2 - 2) * q^91 + (-z^9 - 2z^8 - z^6 + z^5 + 2z^3 + z^2) * q^93 + (4z^8 - 4z^7 + 4z^6 - 2z^5 - z^4 - 2z^3 + 4z^2 - 4z + 4) q^94 + (2z^9 + 4z^8 - 4z^7 - 2z^5 + 2z^4 + 4z^2 - 4z - 2) q^95 + (-z^9 + 5z^8 - z^7 - 4z^5 - 4z^4 + 4z + 4) * q^96 + (-2z^9 + 5z^8 - 5z^7 + 2z^6 + 7z^4 + 6z^2 + 7) * q^97 + (4z^9 - 4z^8 - 2z^6 - 2z^5 - 4z^4 + z^3 - 4z^2 - 2z - 2) q^98 + (-2z^9 - 3z^8 + 3z^7 + z^6 - 3z^5 + z^4 + 3z^3 - 3z^2 - 2z) q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 7 q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} + 6 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) 10 * q - 7 * q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 + 6 * q^7 + 4 * q^8 + 9 * q^9	\( 10 q - 7 q^{2} + 4 q^{3} - 3 q^{4} - 3 q^{5} - 5 q^{6} + 6 q^{7} + 4 q^{8} + 9 q^{9} - 10 q^{10} - 4 q^{11} + 23 q^{12} + 8 q^{13} - 2 q^{14} - 10 q^{15} - 21 q^{16} + q^{17} + 8 q^{18} - 20 q^{19} + 24 q^{20} - 2 q^{21} - 6 q^{22} - 38 q^{24} - 4 q^{25} + q^{26} + 7 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} - q^{31} - q^{32} + 5 q^{33} + 18 q^{34} - 26 q^{35} + 5 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 32 q^{40} + 7 q^{41} + 30 q^{42} + 10 q^{44} - 6 q^{45} - 18 q^{47} - 4 q^{48} + 15 q^{49} - 39 q^{50} - 15 q^{51} - 9 q^{52} - 4 q^{53} - 28 q^{54} - q^{55} - 13 q^{56} - 52 q^{57} - 23 q^{58} + q^{59} - 8 q^{60} + 14 q^{61} + 15 q^{62} - 10 q^{63} + 2 q^{64} + 24 q^{65} - 42 q^{66} - 32 q^{67} - 30 q^{68} + 38 q^{70} + 19 q^{71} - 14 q^{72} + 19 q^{73} - 34 q^{74} + 16 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} + 40 q^{79} + 3 q^{80} + 33 q^{81} - 17 q^{82} - 4 q^{83} - 17 q^{84} + 3 q^{85} + 22 q^{86} - q^{87} - 50 q^{88} + 14 q^{89} + 13 q^{90} - 4 q^{91} + 4 q^{93} + 17 q^{94} - 38 q^{95} + 37 q^{96} + 43 q^{97} - 5 q^{98} + 3 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 + 4 * q^3 - 3 * q^4 - 3 * q^5 - 5 * q^6 + 6 * q^7 + 4 * q^8 + 9 * q^9 - 10 * q^10 - 4 * q^11 + 23 * q^12 + 8 * q^13 - 2 * q^14 - 10 * q^15 - 21 * q^16 + q^17 + 8 * q^18 - 20 * q^19 + 24 * q^20 - 2 * q^21 - 6 * q^22 - 38 * q^24 - 4 * q^25 + q^26 + 7 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 - q^31 - q^32 + 5 * q^33 + 18 * q^34 - 26 * q^35 + 5 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 32 * q^40 + 7 * q^41 + 30 * q^42 + 10 * q^44 - 6 * q^45 - 18 * q^47 - 4 * q^48 + 15 * q^49 - 39 * q^50 - 15 * q^51 - 9 * q^52 - 4 * q^53 - 28 * q^54 - q^55 - 13 * q^56 - 52 * q^57 - 23 * q^58 + q^59 - 8 * q^60 + 14 * q^61 + 15 * q^62 - 10 * q^63 + 2 * q^64 + 24 * q^65 - 42 * q^66 - 32 * q^67 - 30 * q^68 + 38 * q^70 + 19 * q^71 - 14 * q^72 + 19 * q^73 - 34 * q^74 + 16 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 + 40 * q^79 + 3 * q^80 + 33 * q^81 - 17 * q^82 - 4 * q^83 - 17 * q^84 + 3 * q^85 + 22 * q^86 - q^87 - 50 * q^88 + 14 * q^89 + 13 * q^90 - 4 * q^91 + 4 * q^93 + 17 * q^94 - 38 * q^95 + 37 * q^96 + 43 * q^97 - 5 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more