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Properties

Label 1815.2.be
Level $1815$
Weight $2$
Character orbit 1815.be
Rep. character $\chi_{1815}(34,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $1320$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.be (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1815, [\chi])\).

Total New Old
Modular forms 2680 1320 1360
Cusp forms 2600 1320 1280
Eisenstein series 80 0 80

Trace form

\( 1320 q + 132 q^{4} - 4 q^{5} + 4 q^{6} - 1320 q^{9} + O(q^{10}) \) \( 1320 q + 132 q^{4} - 4 q^{5} + 4 q^{6} - 1320 q^{9} + 10 q^{10} - 44 q^{11} + 8 q^{14} - 116 q^{16} - 16 q^{19} - 4 q^{20} + 8 q^{21} - 12 q^{24} + 4 q^{25} + 32 q^{26} - 16 q^{30} + 8 q^{34} - 132 q^{36} - 8 q^{39} + 28 q^{40} - 8 q^{44} + 4 q^{45} - 32 q^{46} + 88 q^{49} - 52 q^{50} + 8 q^{51} - 4 q^{54} + 88 q^{55} + 192 q^{56} - 16 q^{59} - 4 q^{60} + 40 q^{61} + 172 q^{64} - 106 q^{65} - 8 q^{66} + 56 q^{70} - 112 q^{71} - 32 q^{74} + 8 q^{75} - 24 q^{76} - 76 q^{79} + 72 q^{80} + 1320 q^{81} + 48 q^{85} - 16 q^{86} + 40 q^{89} - 10 q^{90} + 128 q^{94} + 48 q^{95} + 28 q^{96} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)