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Properties

Label 1155.2.bc
Level $1155$
Weight $2$
Character orbit 1155.bc
Rep. character $\chi_{1155}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
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 400 192 208
Cusp forms 368 192 176
Eisenstein series 32 0 32

Trace form

\( 192 q - 96 q^{4} - 12 q^{5} - 96 q^{9} + O(q^{10}) \) \( 192 q - 96 q^{4} - 12 q^{5} - 96 q^{9} + 24 q^{14} + 8 q^{15} - 104 q^{16} + 8 q^{25} - 24 q^{26} + 24 q^{31} + 192 q^{36} + 20 q^{44} + 12 q^{45} - 80 q^{56} + 48 q^{59} + 224 q^{64} - 36 q^{66} + 88 q^{70} - 32 q^{71} + 24 q^{75} + 120 q^{80} - 96 q^{81} - 88 q^{86} - 96 q^{91} + O(q^{100}) \)

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

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