Properties

Label 1155.2.dd
Level $1155$
Weight $2$
Character orbit 1155.dd
Rep. character $\chi_{1155}(59,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1472$
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.dd (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1155 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1600 1600 0
Cusp forms 1472 1472 0
Eisenstein series 128 128 0

Trace form

\( 1472 q + 164 q^{4} - 12 q^{9} + O(q^{10}) \) \( 1472 q + 164 q^{4} - 12 q^{9} - 60 q^{10} + 164 q^{16} - 36 q^{19} - 44 q^{21} - 30 q^{24} - 6 q^{25} + 29 q^{30} - 104 q^{36} - 42 q^{39} - 36 q^{40} + 24 q^{45} + 52 q^{46} - 80 q^{49} - 2 q^{51} + 12 q^{54} - 21 q^{60} - 36 q^{61} - 440 q^{64} - 198 q^{66} - 52 q^{70} + 33 q^{75} - 84 q^{79} - 48 q^{81} + 54 q^{84} + 120 q^{85} + 88 q^{91} - 252 q^{94} - 384 q^{96} + 88 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.