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Properties

Label 1155.2.bb
Level $1155$
Weight $2$
Character orbit 1155.bb
Rep. character $\chi_{1155}(296,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
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.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
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 400 256 144
Cusp forms 368 256 112
Eisenstein series 32 0 32

Trace form

\( 256 q - 128 q^{4} + 4 q^{9} + O(q^{10}) \) \( 256 q - 128 q^{4} + 4 q^{9} - 8 q^{15} - 96 q^{16} + 56 q^{22} + 128 q^{25} - 24 q^{27} + 20 q^{33} - 112 q^{34} + 8 q^{36} + 8 q^{37} - 124 q^{42} + 168 q^{48} - 8 q^{55} + 24 q^{58} + 44 q^{60} + 32 q^{64} + 60 q^{66} - 64 q^{67} + 16 q^{69} - 24 q^{70} - 136 q^{78} + 28 q^{81} - 32 q^{82} - 16 q^{88} + 32 q^{91} - 44 q^{93} + 16 q^{97} + 32 q^{99} + O(q^{100}) \)

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

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