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Properties

Label 2475.2.gc
Level $2475$
Weight $2$
Character orbit 2475.gc
Rep. character $\chi_{2475}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $4800$
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.gc (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 5824 4800 1024
Cusp forms 5696 4800 896
Eisenstein series 128 0 128

Trace form

\( 4800 q - 2 q^{3} + O(q^{10}) \) \( 4800 q - 2 q^{3} + 8 q^{12} + 4 q^{15} - 600 q^{16} + 72 q^{18} + 24 q^{20} + 48 q^{23} - 24 q^{25} + 28 q^{27} + 88 q^{30} + 120 q^{32} - 4 q^{33} + 12 q^{37} + 80 q^{39} - 344 q^{42} - 52 q^{45} - 36 q^{47} + 196 q^{48} + 260 q^{54} + 12 q^{55} + 4 q^{57} - 30 q^{59} - 400 q^{60} + 168 q^{63} + 144 q^{65} + 6 q^{67} - 576 q^{68} - 140 q^{69} - 88 q^{72} + 52 q^{75} - 148 q^{78} + 20 q^{81} + 96 q^{82} - 240 q^{84} + 48 q^{85} - 204 q^{87} - 136 q^{90} + 144 q^{92} - 36 q^{93} - 120 q^{95} + 54 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)