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Properties

Label 2805.2.s
Level $2805$
Weight $2$
Character orbit 2805.s
Rep. character $\chi_{2805}(166,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $240$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
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 880 240 640
Cusp forms 848 240 608
Eisenstein series 32 0 32

Trace form

\( 240 q - 240 q^{4} + 8 q^{6} + O(q^{10}) \) \( 240 q - 240 q^{4} + 8 q^{6} - 8 q^{10} + 16 q^{14} + 224 q^{16} + 16 q^{17} - 16 q^{20} - 16 q^{23} - 8 q^{24} - 80 q^{28} - 32 q^{31} + 16 q^{33} - 24 q^{34} + 32 q^{37} + 8 q^{40} + 16 q^{41} + 16 q^{44} - 32 q^{46} - 16 q^{47} + 8 q^{54} - 32 q^{55} + 144 q^{56} - 64 q^{58} + 32 q^{61} + 16 q^{62} - 16 q^{64} + 16 q^{67} + 16 q^{68} - 64 q^{69} + 80 q^{71} - 16 q^{73} + 64 q^{74} - 32 q^{78} + 16 q^{79} + 32 q^{80} - 240 q^{81} - 32 q^{82} - 16 q^{85} - 192 q^{86} - 48 q^{89} - 8 q^{90} + 32 q^{91} - 32 q^{92} - 64 q^{95} + 8 q^{96} + 16 q^{97} - 160 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(2805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(561, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)