Properties

Label 2805.2.r
Level $2805$
Weight $2$
Character orbit 2805.r
Rep. character $\chi_{2805}(956,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $576$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2805.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 561 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2805, [\chi])\).

Total New Old
Modular forms 880 576 304
Cusp forms 848 576 272
Eisenstein series 32 0 32

Trace form

\( 576 q + 8 q^{3} - 576 q^{4} + O(q^{10}) \) \( 576 q + 8 q^{3} - 576 q^{4} - 24 q^{12} + 576 q^{16} - 16 q^{27} + 64 q^{33} + 48 q^{34} + 56 q^{48} + 16 q^{55} + 48 q^{58} - 624 q^{64} - 96 q^{69} + 8 q^{75} - 136 q^{78} + 64 q^{81} - 32 q^{82} - 40 q^{88} + 160 q^{91} - 224 q^{97} + 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2805, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(561, [\chi])\)\(^{\oplus 2}\)