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Properties

Label 2805.2.eg
Level $2805$
Weight $2$
Character orbit 2805.eg
Rep. character $\chi_{2805}(446,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2304$
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.eg (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 561 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3520 2304 1216
Cusp forms 3392 2304 1088
Eisenstein series 128 0 128

Trace form

\( 2304 q - 8 q^{3} + 576 q^{4} + 20 q^{6} + O(q^{10}) \) \( 2304 q - 8 q^{3} + 576 q^{4} + 20 q^{6} + 24 q^{12} - 576 q^{16} - 120 q^{22} + 60 q^{24} - 44 q^{27} + 40 q^{31} + 56 q^{33} - 128 q^{34} - 40 q^{37} + 80 q^{39} + 40 q^{46} - 56 q^{48} + 80 q^{51} - 16 q^{55} - 60 q^{57} + 112 q^{58} + 40 q^{61} - 60 q^{63} + 504 q^{64} + 96 q^{69} + 240 q^{72} + 12 q^{75} - 24 q^{78} - 40 q^{79} - 184 q^{81} + 152 q^{82} - 240 q^{84} + 40 q^{88} + 200 q^{91} - 296 q^{97} + 60 q^{99} + O(q^{100}) \)

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

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