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Properties

Label 1155.2.y
Level $1155$
Weight $2$
Character orbit 1155.y
Rep. character $\chi_{1155}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 400 144 256
Cusp forms 368 144 224
Eisenstein series 32 0 32

Trace form

\( 144 q + O(q^{10}) \) \( 144 q - 32 q^{12} - 144 q^{16} + 80 q^{20} - 64 q^{22} + 16 q^{25} + 32 q^{31} - 8 q^{33} - 144 q^{36} - 16 q^{37} + 112 q^{38} + 64 q^{47} - 64 q^{48} - 48 q^{53} + 48 q^{55} - 96 q^{56} + 88 q^{58} - 64 q^{60} - 16 q^{66} + 64 q^{67} - 16 q^{70} + 32 q^{75} - 16 q^{77} + 24 q^{78} + 80 q^{80} - 144 q^{81} + 176 q^{82} - 32 q^{86} - 120 q^{88} + 48 q^{93} + 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)