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Properties

Label 1155.2.s
Level $1155$
Weight $2$
Character orbit 1155.s
Rep. character $\chi_{1155}(617,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $240$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 240 160
Cusp forms 368 240 128
Eisenstein series 32 0 32

Trace form

\( 240 q + 4 q^{3} + O(q^{10}) \) \( 240 q + 4 q^{3} - 16 q^{12} + 32 q^{13} + 16 q^{15} - 256 q^{16} + 40 q^{18} + 24 q^{25} + 16 q^{27} - 40 q^{30} + 32 q^{31} - 4 q^{33} + 72 q^{37} - 96 q^{40} + 40 q^{42} - 40 q^{45} + 96 q^{46} + 8 q^{48} - 32 q^{51} - 96 q^{52} - 24 q^{55} - 8 q^{57} - 56 q^{58} + 72 q^{60} - 64 q^{61} + 16 q^{63} + 24 q^{67} - 104 q^{72} - 64 q^{73} + 136 q^{75} - 64 q^{76} - 88 q^{78} - 8 q^{81} + 128 q^{82} - 32 q^{85} - 8 q^{87} + 24 q^{88} + 80 q^{90} + 36 q^{93} - 104 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)