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Properties

Label 836.2
Level 836
Weight 2
Dimension 12016
Nonzero newspaces 24
Newform subspaces 45
Sturm bound 86400
Trace bound 7

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Defining parameters

Level: \( N \) = \( 836 = 2^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 45 \)
Sturm bound: \(86400\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(836))\).

Total New Old
Modular forms 22500 12624 9876
Cusp forms 20701 12016 8685
Eisenstein series 1799 608 1191

Trace form

\( 12016 q - 62 q^{2} - 62 q^{4} - 124 q^{5} - 62 q^{6} + 10 q^{7} - 62 q^{8} - 104 q^{9} + O(q^{10}) \) \( 12016 q - 62 q^{2} - 62 q^{4} - 124 q^{5} - 62 q^{6} + 10 q^{7} - 62 q^{8} - 104 q^{9} - 72 q^{10} + 10 q^{11} - 142 q^{12} - 90 q^{13} - 72 q^{14} + 36 q^{15} - 102 q^{16} - 116 q^{17} - 130 q^{18} + 27 q^{19} - 184 q^{20} - 142 q^{21} - 131 q^{22} + 8 q^{23} - 122 q^{24} - 108 q^{25} - 112 q^{26} + 6 q^{27} - 166 q^{28} - 150 q^{29} - 198 q^{30} - 36 q^{31} - 162 q^{32} - 176 q^{33} - 192 q^{34} - 42 q^{35} - 192 q^{36} - 256 q^{37} - 168 q^{38} - 118 q^{39} - 118 q^{40} - 190 q^{41} - 152 q^{42} - 46 q^{43} - 46 q^{44} - 438 q^{45} - 102 q^{46} + 28 q^{47} - 78 q^{48} - 128 q^{49} - 96 q^{50} + 62 q^{51} - 52 q^{52} - 142 q^{53} - 18 q^{54} + 16 q^{55} - 220 q^{56} - 79 q^{57} - 204 q^{58} + 50 q^{59} - 170 q^{60} - 126 q^{61} - 122 q^{62} + 24 q^{63} - 38 q^{64} - 182 q^{65} - 129 q^{66} - 60 q^{67} - 66 q^{68} - 428 q^{69} + 104 q^{70} - 22 q^{71} + 108 q^{72} - 270 q^{73} - 44 q^{74} - 74 q^{75} + 108 q^{76} - 451 q^{77} + 22 q^{78} - 58 q^{79} + 112 q^{80} - 124 q^{81} + 268 q^{82} + 68 q^{83} + 164 q^{84} - 210 q^{85} + 164 q^{86} + 172 q^{87} + 161 q^{88} - 248 q^{89} + 82 q^{90} + 94 q^{91} + 18 q^{92} - 4 q^{93} - 30 q^{94} + 7 q^{95} - 288 q^{96} - 122 q^{97} - 270 q^{98} - 11 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(836))\)

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
836.2.a \(\chi_{836}(1, \cdot)\) 836.2.a.a 1 1
836.2.a.b 1
836.2.a.c 2
836.2.a.d 6
836.2.a.e 6
836.2.b \(\chi_{836}(417, \cdot)\) 836.2.b.a 4 1
836.2.b.b 16
836.2.d \(\chi_{836}(571, \cdot)\) 836.2.d.a 2 1
836.2.d.b 2
836.2.d.c 52
836.2.d.d 52
836.2.g \(\chi_{836}(683, \cdot)\) 836.2.g.a 100 1
836.2.i \(\chi_{836}(45, \cdot)\) 836.2.i.a 2 2
836.2.i.b 2
836.2.i.c 2
836.2.i.d 2
836.2.i.e 2
836.2.i.f 4
836.2.i.g 10
836.2.i.h 12
836.2.j \(\chi_{836}(229, \cdot)\) 836.2.j.a 12 4
836.2.j.b 20
836.2.j.c 40
836.2.k \(\chi_{836}(331, \cdot)\) 836.2.k.a 200 2
836.2.o \(\chi_{836}(65, \cdot)\) 836.2.o.a 40 2
836.2.q \(\chi_{836}(87, \cdot)\) 836.2.q.a 232 2
836.2.r \(\chi_{836}(177, \cdot)\) 836.2.r.a 6 6
836.2.r.b 42
836.2.r.c 48
836.2.t \(\chi_{836}(75, \cdot)\) 836.2.t.a 464 4
836.2.w \(\chi_{836}(39, \cdot)\) 836.2.w.a 216 4
836.2.w.b 216
836.2.y \(\chi_{836}(189, \cdot)\) 836.2.y.a 16 4
836.2.y.b 64
836.2.z \(\chi_{836}(49, \cdot)\) 836.2.z.a 160 8
836.2.bc \(\chi_{836}(43, \cdot)\) 836.2.bc.a 696 6
836.2.bd \(\chi_{836}(67, \cdot)\) 836.2.bd.a 600 6
836.2.bf \(\chi_{836}(21, \cdot)\) 836.2.bf.a 120 6
836.2.bh \(\chi_{836}(7, \cdot)\) 836.2.bh.a 928 8
836.2.bj \(\chi_{836}(145, \cdot)\) 836.2.bj.a 160 8
836.2.bn \(\chi_{836}(27, \cdot)\) 836.2.bn.a 928 8
836.2.bo \(\chi_{836}(5, \cdot)\) 836.2.bo.a 480 24
836.2.bq \(\chi_{836}(13, \cdot)\) 836.2.bq.a 480 24
836.2.bs \(\chi_{836}(3, \cdot)\) 836.2.bs.a 2784 24
836.2.bt \(\chi_{836}(35, \cdot)\) 836.2.bt.a 2784 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(836))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(836)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)\(^{\oplus 2}\)