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Properties

Label 1155.2.ce
Level $1155$
Weight $2$
Character orbit 1155.ce
Rep. character $\chi_{1155}(142,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
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.ce (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 800 384 416
Cusp forms 736 384 352
Eisenstein series 64 0 64

Trace form

\( 384 q + 8 q^{5} + O(q^{10}) \) \( 384 q + 8 q^{5} - 8 q^{11} + 16 q^{15} + 208 q^{16} + 24 q^{22} - 32 q^{23} + 24 q^{25} - 48 q^{26} + 12 q^{33} - 384 q^{36} - 40 q^{37} - 8 q^{42} - 40 q^{47} + 8 q^{55} + 32 q^{56} - 16 q^{58} - 24 q^{66} - 48 q^{67} - 120 q^{70} + 64 q^{71} + 16 q^{75} - 116 q^{77} - 48 q^{78} - 80 q^{80} + 192 q^{81} + 16 q^{82} - 80 q^{86} + 8 q^{88} - 32 q^{91} - 160 q^{92} + 48 q^{93} - 208 q^{97} + O(q^{100}) \)

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

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