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Properties

Label 2075.2.b
Level $2075$
Weight $2$
Character orbit 2075.b
Rep. character $\chi_{2075}(499,\cdot)$
Character field $\Q$
Dimension $124$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2075.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2075, [\chi])\).

Total New Old
Modular forms 216 124 92
Cusp forms 204 124 80
Eisenstein series 12 0 12

Trace form

\( 124 q - 126 q^{4} - 132 q^{9} + O(q^{10}) \) \( 124 q - 126 q^{4} - 132 q^{9} - 4 q^{14} + 130 q^{16} - 4 q^{19} + 24 q^{21} + 32 q^{24} - 16 q^{26} - 28 q^{29} + 12 q^{31} - 36 q^{34} + 162 q^{36} - 8 q^{39} + 16 q^{41} - 4 q^{44} + 4 q^{46} - 96 q^{49} + 24 q^{51} + 12 q^{54} - 8 q^{56} - 12 q^{59} + 32 q^{61} - 210 q^{64} - 104 q^{66} - 36 q^{69} + 24 q^{71} + 72 q^{74} + 84 q^{76} + 40 q^{79} + 140 q^{81} + 8 q^{84} + 48 q^{86} - 32 q^{89} - 36 q^{91} - 20 q^{94} - 148 q^{96} + 92 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2075, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2075, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2075, [\chi]) \cong \)