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Properties

Label 618.2
Level 618
Weight 2
Dimension 2653
Nonzero newspaces 8
Newform subspaces 31
Sturm bound 42432
Trace bound 4

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Defining parameters

Level: \( N \) = \( 618 = 2 \cdot 3 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 31 \)
Sturm bound: \(42432\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(618))\).

Total New Old
Modular forms 11016 2653 8363
Cusp forms 10201 2653 7548
Eisenstein series 815 0 815

Trace form

\( 2653 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 2653 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 32 q^{31} + q^{32} + 12 q^{33} + 18 q^{34} + 48 q^{35} + q^{36} + 38 q^{37} + 20 q^{38} + 14 q^{39} + 6 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} + 48 q^{47} + q^{48} + 57 q^{49} + 31 q^{50} + 18 q^{51} + 14 q^{52} + 54 q^{53} + q^{54} + 72 q^{55} + 8 q^{56} + 20 q^{57} + 30 q^{58} + 60 q^{59} + 6 q^{60} + 62 q^{61} + 32 q^{62} + 8 q^{63} + q^{64} + 84 q^{65} + 12 q^{66} + 68 q^{67} + 18 q^{68} + 24 q^{69} + 48 q^{70} + 72 q^{71} + q^{72} + 74 q^{73} + 38 q^{74} + 31 q^{75} + 20 q^{76} + 96 q^{77} + 14 q^{78} + 80 q^{79} + 6 q^{80} + q^{81} + 42 q^{82} + 84 q^{83} - 26 q^{84} - 300 q^{85} - 160 q^{86} - 174 q^{87} + 12 q^{88} - 318 q^{89} - 96 q^{90} - 772 q^{91} - 180 q^{92} - 376 q^{93} - 360 q^{94} - 492 q^{95} + q^{96} - 786 q^{97} - 759 q^{98} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(618))\)

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
618.2.a \(\chi_{618}(1, \cdot)\) 618.2.a.a 1 1
618.2.a.b 1
618.2.a.c 1
618.2.a.d 1
618.2.a.e 1
618.2.a.f 1
618.2.a.g 1
618.2.a.h 2
618.2.a.i 2
618.2.a.j 2
618.2.a.k 4
618.2.d \(\chi_{618}(617, \cdot)\) 618.2.d.a 36 1
618.2.e \(\chi_{618}(355, \cdot)\) 618.2.e.a 2 2
618.2.e.b 2
618.2.e.c 6
618.2.e.d 8
618.2.e.e 8
618.2.e.f 10
618.2.f \(\chi_{618}(47, \cdot)\) 618.2.f.a 4 2
618.2.f.b 64
618.2.i \(\chi_{618}(13, \cdot)\) 618.2.i.a 16 16
618.2.i.b 32
618.2.i.c 64
618.2.i.d 64
618.2.i.e 80
618.2.j \(\chi_{618}(89, \cdot)\) 618.2.j.a 576 16
618.2.m \(\chi_{618}(7, \cdot)\) 618.2.m.a 128 32
618.2.m.b 128
618.2.m.c 160
618.2.m.d 160
618.2.p \(\chi_{618}(5, \cdot)\) 618.2.p.a 1088 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(618))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(618)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(206))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 2}\)