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Properties

Label 612.2
Level 612
Weight 2
Dimension 4618
Nonzero newspaces 20
Newform subspaces 54
Sturm bound 41472
Trace bound 9

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Defining parameters

Level: \( N \) = \( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 54 \)
Sturm bound: \(41472\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(612))\).

Total New Old
Modular forms 11008 4890 6118
Cusp forms 9729 4618 5111
Eisenstein series 1279 272 1007

Trace form

\( 4618 q - 18 q^{2} - 14 q^{4} - 30 q^{5} - 26 q^{6} + 6 q^{7} - 24 q^{8} - 40 q^{9} + O(q^{10}) \) \( 4618 q - 18 q^{2} - 14 q^{4} - 30 q^{5} - 26 q^{6} + 6 q^{7} - 24 q^{8} - 40 q^{9} - 64 q^{10} - 2 q^{11} - 44 q^{12} - 42 q^{13} - 48 q^{14} - 18 q^{15} - 30 q^{16} - 68 q^{17} - 100 q^{18} - 8 q^{19} - 60 q^{20} - 58 q^{21} - 30 q^{22} - 14 q^{23} - 38 q^{24} - 18 q^{25} + 8 q^{26} - 34 q^{29} + 4 q^{30} + 50 q^{31} + 82 q^{32} - 94 q^{33} + 53 q^{34} + 44 q^{35} + 34 q^{36} - 92 q^{37} + 70 q^{38} + 38 q^{39} + 36 q^{40} + 2 q^{41} + 4 q^{42} + 54 q^{43} + 8 q^{44} - 30 q^{45} - 80 q^{46} + 102 q^{47} - 74 q^{48} + 10 q^{49} - 90 q^{50} + 64 q^{51} - 112 q^{52} + 84 q^{53} - 110 q^{54} + 76 q^{55} - 100 q^{56} + 4 q^{57} - 144 q^{58} + 106 q^{59} - 44 q^{60} + 38 q^{61} - 80 q^{62} + 54 q^{63} - 140 q^{64} + 162 q^{65} - 16 q^{66} + 34 q^{67} - 97 q^{68} - 50 q^{69} - 84 q^{70} + 48 q^{71} + 10 q^{72} + 40 q^{73} - 12 q^{74} + 24 q^{75} - 74 q^{76} + 22 q^{77} - 8 q^{78} + 14 q^{79} - 200 q^{80} - 40 q^{81} - 140 q^{82} - 50 q^{83} - 172 q^{84} - 190 q^{85} - 330 q^{86} - 78 q^{87} - 174 q^{88} - 240 q^{89} - 284 q^{90} - 228 q^{91} - 408 q^{92} - 282 q^{93} - 276 q^{94} - 296 q^{95} - 360 q^{96} - 222 q^{97} - 432 q^{98} - 162 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(612))\)

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
612.2.a \(\chi_{612}(1, \cdot)\) 612.2.a.a 1 1
612.2.a.b 1
612.2.a.c 1
612.2.a.d 1
612.2.a.e 2
612.2.b \(\chi_{612}(577, \cdot)\) 612.2.b.a 2 1
612.2.b.b 2
612.2.b.c 4
612.2.c \(\chi_{612}(35, \cdot)\) 612.2.c.a 32 1
612.2.h \(\chi_{612}(611, \cdot)\) 612.2.h.a 4 1
612.2.h.b 32
612.2.i \(\chi_{612}(205, \cdot)\) 612.2.i.a 2 2
612.2.i.b 2
612.2.i.c 4
612.2.i.d 10
612.2.i.e 14
612.2.k \(\chi_{612}(217, \cdot)\) 612.2.k.a 2 2
612.2.k.b 2
612.2.k.c 4
612.2.k.d 4
612.2.k.e 4
612.2.m \(\chi_{612}(251, \cdot)\) 612.2.m.a 4 2
612.2.m.b 4
612.2.m.c 64
612.2.n \(\chi_{612}(203, \cdot)\) 612.2.n.a 16 2
612.2.n.b 192
612.2.s \(\chi_{612}(239, \cdot)\) 612.2.s.a 192 2
612.2.t \(\chi_{612}(169, \cdot)\) 612.2.t.a 16 2
612.2.t.b 20
612.2.w \(\chi_{612}(145, \cdot)\) 612.2.w.a 4 4
612.2.w.b 8
612.2.w.c 16
612.2.x \(\chi_{612}(179, \cdot)\) 612.2.x.a 4 4
612.2.x.b 4
612.2.x.c 4
612.2.x.d 4
612.2.x.e 8
612.2.x.f 8
612.2.x.g 56
612.2.x.h 56
612.2.z \(\chi_{612}(13, \cdot)\) 612.2.z.a 72 4
612.2.bb \(\chi_{612}(47, \cdot)\) 612.2.bb.a 416 4
612.2.bc \(\chi_{612}(125, \cdot)\) 612.2.bc.a 24 8
612.2.bc.b 24
612.2.bd \(\chi_{612}(91, \cdot)\) 612.2.bd.a 8 8
612.2.bd.b 8
612.2.bd.c 8
612.2.bd.d 48
612.2.bd.e 128
612.2.bd.f 144
612.2.bi \(\chi_{612}(25, \cdot)\) 612.2.bi.a 144 8
612.2.bj \(\chi_{612}(59, \cdot)\) 612.2.bj.a 832 8
612.2.bk \(\chi_{612}(7, \cdot)\) 612.2.bk.a 1664 16
612.2.bl \(\chi_{612}(5, \cdot)\) 612.2.bl.a 288 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(612))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(612)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 2}\)