Properties

Label 276.2
Level 276
Weight 2
Dimension 880
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 8448
Trace bound 1

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Defining parameters

Level: \( N \) = \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(8448\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(276))\).

Total New Old
Modular forms 2332 960 1372
Cusp forms 1893 880 1013
Eisenstein series 439 80 359

Trace form

\( 880 q - 22 q^{4} - 11 q^{6} - 22 q^{9} + O(q^{10}) \) \( 880 q - 22 q^{4} - 11 q^{6} - 22 q^{9} - 22 q^{10} - 11 q^{12} - 44 q^{13} + 11 q^{15} - 22 q^{16} + 22 q^{17} - 11 q^{18} + 22 q^{19} + 11 q^{21} - 44 q^{22} + 44 q^{23} - 22 q^{24} + 33 q^{27} - 22 q^{28} + 22 q^{29} - 11 q^{30} + 22 q^{31} - 11 q^{33} - 66 q^{34} - 44 q^{35} - 33 q^{36} - 132 q^{37} - 110 q^{38} - 44 q^{39} - 198 q^{40} - 44 q^{41} - 121 q^{42} - 88 q^{43} - 154 q^{44} - 44 q^{45} - 198 q^{46} - 88 q^{47} - 99 q^{48} - 176 q^{49} - 154 q^{50} - 44 q^{51} - 242 q^{52} - 44 q^{53} - 33 q^{54} - 88 q^{55} - 110 q^{56} - 99 q^{57} - 132 q^{58} - 44 q^{59} - 33 q^{60} - 44 q^{61} - 55 q^{63} - 22 q^{64} + 22 q^{66} - 77 q^{69} - 44 q^{70} - 11 q^{72} - 44 q^{73} + 22 q^{74} - 99 q^{75} + 88 q^{76} - 176 q^{77} + 99 q^{78} - 44 q^{79} + 198 q^{80} - 198 q^{81} + 110 q^{82} - 44 q^{83} + 143 q^{84} - 352 q^{85} + 220 q^{86} - 66 q^{87} + 154 q^{88} - 132 q^{89} + 220 q^{90} - 88 q^{91} + 198 q^{92} - 308 q^{93} + 132 q^{94} - 66 q^{95} + 198 q^{96} - 110 q^{97} + 176 q^{98} - 44 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
276.2.a \(\chi_{276}(1, \cdot)\) 276.2.a.a 2 1
276.2.a.b 2
276.2.c \(\chi_{276}(47, \cdot)\) 276.2.c.a 22 1
276.2.c.b 22
276.2.e \(\chi_{276}(91, \cdot)\) 276.2.e.a 24 1
276.2.g \(\chi_{276}(137, \cdot)\) 276.2.g.a 8 1
276.2.i \(\chi_{276}(13, \cdot)\) 276.2.i.a 20 10
276.2.i.b 20
276.2.k \(\chi_{276}(5, \cdot)\) 276.2.k.a 80 10
276.2.m \(\chi_{276}(7, \cdot)\) 276.2.m.a 240 10
276.2.o \(\chi_{276}(35, \cdot)\) 276.2.o.a 440 10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(276))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(276)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)