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Properties

Label 944.2
Level 944
Weight 2
Dimension 15395
Nonzero newspaces 8
Newform subspaces 33
Sturm bound 111360
Trace bound 2

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Defining parameters

Level: \( N \) = \( 944 = 2^{4} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 33 \)
Sturm bound: \(111360\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(944))\).

Total New Old
Modular forms 28652 15907 12745
Cusp forms 27029 15395 11634
Eisenstein series 1623 512 1111

Trace form

\( 15395 q - 112 q^{2} - 83 q^{3} - 116 q^{4} - 141 q^{5} - 124 q^{6} - 87 q^{7} - 124 q^{8} - 29 q^{9} + O(q^{10}) \) \( 15395 q - 112 q^{2} - 83 q^{3} - 116 q^{4} - 141 q^{5} - 124 q^{6} - 87 q^{7} - 124 q^{8} - 29 q^{9} - 116 q^{10} - 91 q^{11} - 108 q^{12} - 141 q^{13} - 108 q^{14} - 95 q^{15} - 100 q^{16} - 253 q^{17} - 120 q^{18} - 99 q^{19} - 124 q^{20} - 153 q^{21} - 116 q^{22} - 87 q^{23} - 116 q^{24} - 29 q^{25} - 124 q^{26} - 71 q^{27} - 132 q^{28} - 157 q^{29} - 108 q^{30} - 55 q^{31} - 132 q^{32} - 253 q^{33} - 124 q^{34} - 79 q^{35} - 108 q^{36} - 157 q^{37} - 92 q^{38} - 87 q^{39} - 100 q^{40} - 29 q^{41} - 116 q^{42} - 107 q^{43} - 108 q^{44} - 149 q^{45} - 140 q^{46} - 119 q^{47} - 132 q^{48} - 273 q^{49} - 104 q^{50} - 95 q^{51} - 108 q^{52} - 125 q^{53} - 116 q^{54} - 87 q^{55} - 100 q^{56} - 29 q^{57} - 92 q^{58} - 81 q^{59} - 232 q^{60} - 109 q^{61} - 148 q^{62} - 95 q^{63} - 116 q^{64} - 269 q^{65} - 124 q^{66} - 67 q^{67} - 116 q^{68} - 121 q^{69} - 132 q^{70} - 87 q^{71} - 124 q^{72} - 29 q^{73} - 116 q^{74} - 99 q^{75} - 140 q^{76} - 153 q^{77} - 108 q^{78} - 87 q^{79} - 132 q^{80} - 281 q^{81} - 116 q^{82} - 83 q^{83} - 100 q^{84} - 153 q^{85} - 116 q^{86} - 87 q^{87} - 132 q^{88} - 29 q^{89} - 108 q^{90} - 95 q^{91} - 68 q^{92} - 177 q^{93} - 84 q^{94} - 63 q^{95} - 84 q^{96} - 253 q^{97} - 104 q^{98} - 83 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(944))\)

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
944.2.a \(\chi_{944}(1, \cdot)\) 944.2.a.a 1 1
944.2.a.b 1
944.2.a.c 1
944.2.a.d 1
944.2.a.e 1
944.2.a.f 1
944.2.a.g 1
944.2.a.h 1
944.2.a.i 1
944.2.a.j 1
944.2.a.k 1
944.2.a.l 3
944.2.a.m 4
944.2.a.n 5
944.2.a.o 6
944.2.b \(\chi_{944}(473, \cdot)\) None 0 1
944.2.e \(\chi_{944}(943, \cdot)\) 944.2.e.a 4 1
944.2.e.b 4
944.2.e.c 4
944.2.e.d 6
944.2.e.e 12
944.2.f \(\chi_{944}(471, \cdot)\) None 0 1
944.2.i \(\chi_{944}(237, \cdot)\) 944.2.i.a 4 2
944.2.i.b 228
944.2.k \(\chi_{944}(235, \cdot)\) 944.2.k.a 236 2
944.2.m \(\chi_{944}(17, \cdot)\) 944.2.m.a 56 28
944.2.m.b 84
944.2.m.c 112
944.2.m.d 140
944.2.m.e 196
944.2.m.f 224
944.2.p \(\chi_{944}(23, \cdot)\) None 0 28
944.2.q \(\chi_{944}(31, \cdot)\) 944.2.q.a 280 28
944.2.q.b 560
944.2.t \(\chi_{944}(9, \cdot)\) None 0 28
944.2.v \(\chi_{944}(11, \cdot)\) 944.2.v.a 6608 56
944.2.x \(\chi_{944}(5, \cdot)\) 944.2.x.a 6608 56

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(944))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(944)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(944))\)\(^{\oplus 1}\)