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Properties

Label 1155.2.cc
Level $1155$
Weight $2$
Character orbit 1155.cc
Rep. character $\chi_{1155}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $288$
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.cc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
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 800 288 512
Cusp forms 736 288 448
Eisenstein series 64 0 64

Trace form

\( 288 q + 72 q^{4} + 72 q^{9} + O(q^{10}) \) \( 288 q + 72 q^{4} + 72 q^{9} + 16 q^{10} - 8 q^{15} - 24 q^{16} + 16 q^{19} - 60 q^{20} + 32 q^{21} + 120 q^{26} - 16 q^{30} + 16 q^{31} - 16 q^{34} - 72 q^{36} + 16 q^{39} + 108 q^{40} + 152 q^{44} - 144 q^{46} + 72 q^{49} + 76 q^{50} - 32 q^{51} - 32 q^{55} + 48 q^{56} - 72 q^{59} - 60 q^{60} - 32 q^{61} - 48 q^{64} - 8 q^{65} - 48 q^{66} - 24 q^{69} - 4 q^{70} - 16 q^{71} - 48 q^{74} + 64 q^{75} - 144 q^{76} + 104 q^{79} - 96 q^{80} - 72 q^{81} + 24 q^{84} + 28 q^{85} - 32 q^{89} + 24 q^{90} - 184 q^{94} + 64 q^{95} + O(q^{100}) \)

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

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