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Properties

Label 2005.2.d
Level $2005$
Weight $2$
Character orbit 2005.d
Rep. character $\chi_{2005}(801,\cdot)$
Character field $\Q$
Dimension $134$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 401 \)
Character field: \(\Q\)
Sturm bound: \(402\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2005, [\chi])\).

Total New Old
Modular forms 202 134 68
Cusp forms 198 134 64
Eisenstein series 4 0 4

Trace form

\( 134 q - 6 q^{2} + 138 q^{4} + 2 q^{5} - 4 q^{7} - 18 q^{8} - 114 q^{9} + O(q^{10}) \) \( 134 q - 6 q^{2} + 138 q^{4} + 2 q^{5} - 4 q^{7} - 18 q^{8} - 114 q^{9} - 2 q^{10} + 8 q^{11} - 32 q^{14} + 170 q^{16} + 42 q^{18} - 2 q^{20} - 32 q^{22} + 134 q^{25} - 8 q^{28} - 24 q^{29} - 2 q^{32} - 4 q^{35} - 98 q^{36} - 12 q^{39} - 6 q^{40} - 20 q^{41} - 12 q^{43} + 32 q^{44} + 6 q^{45} - 44 q^{47} + 150 q^{49} - 6 q^{50} + 56 q^{51} - 56 q^{56} + 40 q^{57} - 8 q^{58} - 16 q^{63} + 162 q^{64} - 16 q^{69} + 24 q^{70} - 2 q^{72} + 12 q^{73} + 16 q^{77} - 188 q^{78} - 2 q^{80} + 166 q^{81} + 60 q^{83} - 148 q^{86} - 196 q^{88} - 36 q^{89} + 10 q^{90} + 4 q^{93} + 24 q^{94} + 66 q^{98} + 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2005, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2005, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2005, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(401, [\chi])\)\(^{\oplus 2}\)