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Properties

Label 1155.2.bz
Level $1155$
Weight $2$
Character orbit 1155.bz
Rep. character $\chi_{1155}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
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.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 800 576 224
Cusp forms 736 576 160
Eisenstein series 64 0 64

Trace form

\( 576 q + 144 q^{4} + 2 q^{9} + O(q^{10}) \) \( 576 q + 144 q^{4} + 2 q^{9} + 10 q^{15} - 96 q^{16} - 36 q^{25} - 60 q^{30} - 8 q^{31} + 16 q^{34} - 16 q^{36} + 40 q^{39} + 96 q^{45} - 40 q^{46} - 144 q^{49} - 40 q^{51} - 28 q^{55} - 88 q^{60} + 72 q^{64} - 84 q^{66} - 108 q^{69} - 4 q^{70} + 46 q^{75} - 40 q^{79} + 18 q^{81} - 40 q^{84} + 60 q^{85} - 100 q^{90} + 36 q^{91} + 160 q^{96} - 130 q^{99} + O(q^{100}) \)

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

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