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Properties

Label 1155.2.bg
Level $1155$
Weight $2$
Character orbit 1155.bg
Rep. character $\chi_{1155}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 320 80
Cusp forms 368 320 48
Eisenstein series 32 0 32

Trace form

\( 320 q - 160 q^{4} + 4 q^{9} + O(q^{10}) \) \( 320 q - 160 q^{4} + 4 q^{9} + 28 q^{15} - 160 q^{16} - 24 q^{19} + 16 q^{21} - 36 q^{24} - 40 q^{30} - 104 q^{36} + 16 q^{39} + 60 q^{40} - 18 q^{45} - 64 q^{46} - 16 q^{49} - 24 q^{51} - 28 q^{60} - 96 q^{61} + 272 q^{64} - 124 q^{70} - 72 q^{75} - 32 q^{79} - 20 q^{81} - 60 q^{84} - 56 q^{85} + 64 q^{91} + 96 q^{94} + 84 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)