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Properties

Label 2475.2.eg
Level $2475$
Weight $2$
Character orbit 2475.eg
Rep. character $\chi_{2475}(49,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1696$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.eg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 495 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 2976 1760 1216
Cusp forms 2784 1696 1088
Eisenstein series 192 64 128

Trace form

\( 1696 q - 202 q^{4} - 20 q^{6} - 10 q^{9} + O(q^{10}) \) \( 1696 q - 202 q^{4} - 20 q^{6} - 10 q^{9} - 12 q^{11} + 22 q^{14} + 202 q^{16} + 24 q^{19} - 36 q^{21} - 40 q^{24} + 24 q^{26} + 14 q^{29} + 8 q^{34} - 36 q^{36} - 120 q^{39} - 38 q^{41} + 88 q^{44} - 182 q^{49} - 4 q^{51} + 244 q^{54} - 68 q^{56} + 22 q^{59} - 6 q^{61} + 400 q^{64} + 92 q^{66} + 72 q^{69} + 20 q^{71} + 238 q^{74} - 16 q^{76} + 54 q^{79} - 14 q^{81} - 198 q^{84} + 264 q^{89} - 152 q^{91} + 70 q^{94} - 74 q^{96} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)