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Properties

Label 1155.2.cn
Level $1155$
Weight $2$
Character orbit 1155.cn
Rep. character $\chi_{1155}(127,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $576$
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.cn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1600 576 1024
Cusp forms 1472 576 896
Eisenstein series 128 0 128

Trace form

\( 576 q + O(q^{10}) \) \( 576 q + 32 q^{12} + 144 q^{16} + 120 q^{20} + 64 q^{22} + 24 q^{25} + 80 q^{30} - 32 q^{31} + 8 q^{33} + 144 q^{36} + 16 q^{37} - 112 q^{38} + 160 q^{46} - 64 q^{47} - 96 q^{48} - 160 q^{50} - 80 q^{52} - 72 q^{53} - 128 q^{55} + 96 q^{56} - 80 q^{57} - 88 q^{58} - 96 q^{60} - 160 q^{62} - 64 q^{66} - 64 q^{67} + 16 q^{70} - 32 q^{75} + 16 q^{77} + 96 q^{78} - 80 q^{80} + 144 q^{81} - 96 q^{82} + 400 q^{83} + 80 q^{85} + 32 q^{86} + 200 q^{88} - 200 q^{92} + 72 q^{93} - 160 q^{95} - 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)