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Properties

Label 1155.2.cm
Level $1155$
Weight $2$
Character orbit 1155.cm
Rep. character $\chi_{1155}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $512$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.cm (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1155, [\chi])\).

Total New Old
Modular forms 1600 512 1088
Cusp forms 1472 512 960
Eisenstein series 128 0 128

Trace form

\( 512 q - 8 q^{2} + 56 q^{4} - 32 q^{8} + 64 q^{9} + O(q^{10}) \) \( 512 q - 8 q^{2} + 56 q^{4} - 32 q^{8} + 64 q^{9} + 32 q^{10} - 4 q^{11} + 32 q^{13} + 12 q^{14} + 88 q^{16} - 24 q^{17} + 12 q^{18} + 8 q^{19} - 16 q^{20} + 96 q^{22} - 16 q^{23} - 36 q^{24} + 64 q^{25} - 8 q^{26} - 24 q^{28} + 112 q^{29} - 16 q^{32} + 224 q^{34} - 8 q^{35} - 112 q^{36} + 56 q^{37} + 16 q^{38} - 24 q^{40} + 72 q^{41} - 8 q^{42} + 32 q^{43} + 8 q^{44} + 12 q^{46} + 8 q^{47} - 64 q^{49} + 16 q^{50} - 12 q^{51} - 24 q^{52} + 104 q^{53} - 8 q^{55} + 12 q^{58} - 16 q^{59} + 72 q^{61} - 96 q^{62} - 184 q^{64} + 24 q^{65} + 12 q^{66} - 48 q^{67} - 72 q^{68} - 32 q^{69} + 52 q^{70} - 128 q^{71} - 4 q^{72} - 68 q^{73} - 56 q^{74} + 48 q^{76} - 36 q^{77} - 48 q^{78} - 4 q^{79} + 16 q^{80} + 64 q^{81} - 16 q^{82} - 192 q^{83} + 48 q^{84} + 180 q^{86} + 192 q^{87} - 88 q^{88} - 96 q^{89} + 16 q^{90} + 84 q^{91} - 440 q^{92} + 16 q^{93} + 156 q^{94} + 48 q^{96} - 96 q^{97} - 32 q^{98} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)