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Properties

Label 522.2
Level 522
Weight 2
Dimension 1991
Nonzero newspaces 12
Newform subspaces 50
Sturm bound 30240
Trace bound 10

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Defining parameters

Level: \( N \) = \( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 50 \)
Sturm bound: \(30240\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(522))\).

Total New Old
Modular forms 8008 1991 6017
Cusp forms 7113 1991 5122
Eisenstein series 895 0 895

Trace form

\( 1991 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 1991 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} + 7 q^{20} - 12 q^{21} + 22 q^{22} + 16 q^{23} + 6 q^{24} + 46 q^{25} + 27 q^{26} - 8 q^{28} + 62 q^{29} + 48 q^{31} + 2 q^{32} + 18 q^{33} + 29 q^{34} + 56 q^{35} - 6 q^{36} + 44 q^{37} + 26 q^{38} + 7 q^{40} + 18 q^{41} - 2 q^{43} + 12 q^{44} + 24 q^{46} + 16 q^{47} - 6 q^{48} + 50 q^{49} - 10 q^{50} - 18 q^{51} + 4 q^{52} + 15 q^{53} - 18 q^{54} + 112 q^{55} + 4 q^{56} - 6 q^{57} + 6 q^{58} + 34 q^{59} + 72 q^{61} + 16 q^{62} + 24 q^{63} - 4 q^{64} + 63 q^{65} + 66 q^{67} - 6 q^{68} - 84 q^{70} - 176 q^{71} - 6 q^{72} - 177 q^{73} - 260 q^{74} - 250 q^{75} - 170 q^{76} - 432 q^{77} - 212 q^{78} - 176 q^{79} - 430 q^{81} - 204 q^{82} - 312 q^{83} - 156 q^{84} - 504 q^{85} - 422 q^{86} - 298 q^{87} - 6 q^{88} - 444 q^{89} - 280 q^{90} - 520 q^{91} - 264 q^{92} - 224 q^{93} - 180 q^{94} - 672 q^{95} - 151 q^{97} - 324 q^{98} - 316 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
522.2.a \(\chi_{522}(1, \cdot)\) 522.2.a.a 1 1
522.2.a.b 1
522.2.a.c 1
522.2.a.d 1
522.2.a.e 1
522.2.a.f 1
522.2.a.g 1
522.2.a.h 1
522.2.a.i 1
522.2.a.j 1
522.2.a.k 1
522.2.a.l 1
522.2.a.m 1
522.2.d \(\chi_{522}(289, \cdot)\) 522.2.d.a 2 1
522.2.d.b 2
522.2.d.c 4
522.2.d.d 4
522.2.e \(\chi_{522}(175, \cdot)\) 522.2.e.a 2 2
522.2.e.b 2
522.2.e.c 2
522.2.e.d 2
522.2.e.e 4
522.2.e.f 6
522.2.e.g 8
522.2.e.h 12
522.2.e.i 18
522.2.g \(\chi_{522}(17, \cdot)\) 522.2.g.a 8 2
522.2.g.b 12
522.2.h \(\chi_{522}(115, \cdot)\) 522.2.h.a 4 2
522.2.h.b 56
522.2.k \(\chi_{522}(181, \cdot)\) 522.2.k.a 6 6
522.2.k.b 6
522.2.k.c 6
522.2.k.d 6
522.2.k.e 6
522.2.k.f 12
522.2.k.g 12
522.2.k.h 12
522.2.k.i 12
522.2.l \(\chi_{522}(41, \cdot)\) 522.2.l.a 120 4
522.2.n \(\chi_{522}(91, \cdot)\) 522.2.n.a 12 6
522.2.n.b 12
522.2.n.c 24
522.2.n.d 24
522.2.q \(\chi_{522}(7, \cdot)\) 522.2.q.a 180 12
522.2.q.b 180
522.2.r \(\chi_{522}(89, \cdot)\) 522.2.r.a 48 12
522.2.r.b 72
522.2.v \(\chi_{522}(13, \cdot)\) 522.2.v.a 360 12
522.2.x \(\chi_{522}(11, \cdot)\) 522.2.x.a 720 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(522))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(522)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)