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Properties

Label 246.2
Level 246
Weight 2
Dimension 421
Nonzero newspaces 8
Newform subspaces 30
Sturm bound 6720
Trace bound 5

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Defining parameters

Level: \( N \) = \( 246 = 2 \cdot 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 30 \)
Sturm bound: \(6720\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(246))\).

Total New Old
Modular forms 1840 421 1419
Cusp forms 1521 421 1100
Eisenstein series 319 0 319

Trace form

\( 421 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 421 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} - 34 q^{30} - 48 q^{31} - 19 q^{32} - 108 q^{33} - 82 q^{34} - 112 q^{35} - 19 q^{36} - 202 q^{37} - 60 q^{38} - 146 q^{39} - 74 q^{40} - 39 q^{41} - 152 q^{42} - 36 q^{43} - 68 q^{44} - 154 q^{45} - 56 q^{46} - 192 q^{47} - 19 q^{48} - 103 q^{49} - 69 q^{50} - 102 q^{51} - 6 q^{52} - 26 q^{53} - 39 q^{54} + 72 q^{55} + 8 q^{56} + 20 q^{57} + 30 q^{58} + 60 q^{59} + 6 q^{60} + 62 q^{61} + 32 q^{62} + 8 q^{63} + q^{64} + 64 q^{65} + 12 q^{66} - 52 q^{67} + 18 q^{68} - 56 q^{69} + 48 q^{70} - 88 q^{71} + q^{72} - 86 q^{73} + 38 q^{74} - 129 q^{75} + 20 q^{76} - 64 q^{77} + 14 q^{78} - 80 q^{79} + 6 q^{80} - 19 q^{81} + 41 q^{82} - 76 q^{83} + 8 q^{84} - 232 q^{85} + 44 q^{86} - 50 q^{87} + 12 q^{88} - 70 q^{89} + 6 q^{90} - 208 q^{91} + 24 q^{92} - 48 q^{93} + 48 q^{94} - 40 q^{95} + q^{96} - 62 q^{97} + 57 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)

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
246.2.a \(\chi_{246}(1, \cdot)\) 246.2.a.a 1 1
246.2.a.b 1
246.2.a.c 1
246.2.a.d 1
246.2.a.e 1
246.2.a.f 1
246.2.a.g 1
246.2.d \(\chi_{246}(163, \cdot)\) 246.2.d.a 2 1
246.2.d.b 4
246.2.e \(\chi_{246}(73, \cdot)\) 246.2.e.a 8 2
246.2.e.b 8
246.2.g \(\chi_{246}(37, \cdot)\) 246.2.g.a 4 4
246.2.g.b 4
246.2.g.c 4
246.2.g.d 4
246.2.g.e 8
246.2.i \(\chi_{246}(137, \cdot)\) 246.2.i.a 4 4
246.2.i.b 4
246.2.i.c 4
246.2.i.d 4
246.2.i.e 8
246.2.i.f 8
246.2.i.g 12
246.2.i.h 12
246.2.j \(\chi_{246}(25, \cdot)\) 246.2.j.a 8 4
246.2.j.b 16
246.2.n \(\chi_{246}(43, \cdot)\) 246.2.n.a 32 8
246.2.n.b 32
246.2.o \(\chi_{246}(11, \cdot)\) 246.2.o.a 112 16
246.2.o.b 112

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(246))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(246)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 2}\)