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Properties

Label 2805.2.bo
Level $2805$
Weight $2$
Character orbit 2805.bo
Rep. character $\chi_{2805}(256,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $512$
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.bo (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1760 512 1248
Cusp forms 1696 512 1184
Eisenstein series 64 0 64

Trace form

\( 512 q - 16 q^{2} - 144 q^{4} - 16 q^{7} + 32 q^{8} - 128 q^{9} + O(q^{10}) \) \( 512 q - 16 q^{2} - 144 q^{4} - 16 q^{7} + 32 q^{8} - 128 q^{9} + 32 q^{10} - 24 q^{11} + 48 q^{14} - 96 q^{16} + 24 q^{18} - 16 q^{19} - 16 q^{22} + 32 q^{23} - 128 q^{25} - 32 q^{26} - 8 q^{28} - 64 q^{29} - 16 q^{31} - 32 q^{32} - 16 q^{35} - 144 q^{36} + 96 q^{37} - 16 q^{38} - 24 q^{40} + 72 q^{41} - 32 q^{43} - 32 q^{44} - 8 q^{46} - 24 q^{47} - 64 q^{49} - 16 q^{50} + 88 q^{53} - 96 q^{56} - 16 q^{57} - 40 q^{58} - 24 q^{59} + 48 q^{61} - 16 q^{63} - 44 q^{64} - 48 q^{65} - 28 q^{66} + 36 q^{70} - 16 q^{71} - 8 q^{72} + 88 q^{73} + 48 q^{74} - 152 q^{76} - 88 q^{77} - 80 q^{78} + 48 q^{79} - 128 q^{81} + 184 q^{82} + 72 q^{83} - 24 q^{84} - 8 q^{85} + 144 q^{86} - 64 q^{88} + 96 q^{89} - 8 q^{90} - 72 q^{91} + 224 q^{92} - 64 q^{93} - 16 q^{94} + 120 q^{96} - 80 q^{97} - 192 q^{98} + 56 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(561, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)