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Properties

Label 296.2
Level 296
Weight 2
Dimension 1467
Nonzero newspaces 15
Newform subspaces 26
Sturm bound 10944
Trace bound 6

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Defining parameters

Level: \( N \) = \( 296 = 2^{3} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 26 \)
Sturm bound: \(10944\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(296))\).

Total New Old
Modular forms 2952 1607 1345
Cusp forms 2521 1467 1054
Eisenstein series 431 140 291

Trace form

\( 1467 q - 36 q^{2} - 36 q^{3} - 36 q^{4} - 36 q^{6} - 36 q^{7} - 36 q^{8} - 72 q^{9} + O(q^{10}) \) \( 1467 q - 36 q^{2} - 36 q^{3} - 36 q^{4} - 36 q^{6} - 36 q^{7} - 36 q^{8} - 72 q^{9} - 36 q^{10} - 36 q^{11} - 36 q^{12} - 36 q^{14} - 36 q^{15} - 36 q^{16} - 72 q^{17} - 36 q^{18} - 36 q^{19} - 36 q^{20} - 36 q^{22} - 36 q^{23} - 36 q^{24} - 72 q^{25} - 36 q^{26} - 36 q^{27} - 36 q^{28} - 36 q^{30} - 36 q^{31} - 36 q^{32} - 72 q^{33} - 36 q^{34} - 36 q^{35} - 36 q^{36} - 72 q^{38} - 36 q^{39} - 36 q^{40} - 72 q^{41} - 36 q^{42} - 36 q^{43} - 36 q^{44} - 36 q^{46} - 36 q^{47} - 36 q^{48} - 72 q^{49} - 36 q^{50} - 36 q^{51} - 36 q^{52} - 36 q^{54} - 36 q^{55} - 36 q^{56} - 72 q^{57} - 36 q^{58} - 72 q^{59} - 36 q^{60} - 45 q^{61} - 36 q^{62} - 144 q^{63} - 36 q^{64} - 153 q^{65} - 36 q^{66} - 72 q^{67} - 36 q^{68} - 144 q^{69} - 36 q^{70} - 108 q^{71} - 36 q^{72} - 144 q^{73} - 36 q^{74} - 252 q^{75} - 36 q^{76} - 72 q^{77} - 36 q^{78} - 108 q^{79} - 36 q^{80} - 216 q^{81} - 36 q^{82} - 72 q^{83} - 36 q^{84} - 81 q^{85} - 36 q^{86} - 144 q^{87} - 36 q^{88} - 117 q^{89} - 36 q^{90} - 72 q^{91} - 36 q^{92} - 36 q^{94} - 36 q^{95} - 36 q^{96} - 72 q^{97} - 36 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)

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
296.2.a \(\chi_{296}(1, \cdot)\) 296.2.a.a 1 1
296.2.a.b 1
296.2.a.c 3
296.2.a.d 4
296.2.c \(\chi_{296}(149, \cdot)\) 296.2.c.a 4 1
296.2.c.b 4
296.2.c.c 28
296.2.e \(\chi_{296}(221, \cdot)\) 296.2.e.a 36 1
296.2.g \(\chi_{296}(73, \cdot)\) 296.2.g.a 10 1
296.2.i \(\chi_{296}(121, \cdot)\) 296.2.i.a 2 2
296.2.i.b 6
296.2.i.c 10
296.2.j \(\chi_{296}(43, \cdot)\) 296.2.j.a 8 2
296.2.j.b 64
296.2.l \(\chi_{296}(31, \cdot)\) None 0 2
296.2.o \(\chi_{296}(233, \cdot)\) 296.2.o.a 20 2
296.2.q \(\chi_{296}(85, \cdot)\) 296.2.q.a 72 2
296.2.s \(\chi_{296}(269, \cdot)\) 296.2.s.a 72 2
296.2.u \(\chi_{296}(9, \cdot)\) 296.2.u.a 24 6
296.2.u.b 30
296.2.w \(\chi_{296}(23, \cdot)\) None 0 4
296.2.y \(\chi_{296}(51, \cdot)\) 296.2.y.a 4 4
296.2.y.b 4
296.2.y.c 136
296.2.ba \(\chi_{296}(25, \cdot)\) 296.2.ba.a 60 6
296.2.bc \(\chi_{296}(53, \cdot)\) 296.2.bc.a 216 6
296.2.bf \(\chi_{296}(21, \cdot)\) 296.2.bf.a 216 6
296.2.bh \(\chi_{296}(15, \cdot)\) None 0 12
296.2.bj \(\chi_{296}(19, \cdot)\) 296.2.bj.a 432 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(296))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(296)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 1}\)