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Properties

Label 2475.4.gc
Level $2475$
Weight $4$
Character orbit 2475.gc
Rep. character $\chi_{2475}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $14400$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.gc (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 17344 14400 2944
Cusp forms 17216 14400 2816
Eisenstein series 128 0 128

Trace form

\( 14400 q + 4 q^{3} + O(q^{10}) \) \( 14400 q + 4 q^{3} - 64 q^{12} - 176 q^{15} - 28800 q^{16} - 984 q^{18} + 384 q^{20} + 624 q^{23} + 576 q^{25} - 224 q^{27} - 1832 q^{30} - 2760 q^{32} - 352 q^{33} + 144 q^{37} + 4880 q^{39} - 2768 q^{42} + 848 q^{45} + 4608 q^{47} - 6452 q^{48} - 7540 q^{54} + 792 q^{55} - 5072 q^{57} - 4980 q^{59} - 21760 q^{60} + 2784 q^{63} - 4176 q^{65} + 612 q^{67} + 18432 q^{68} + 6160 q^{69} + 18344 q^{72} - 11888 q^{75} + 7076 q^{78} - 640 q^{81} - 7488 q^{82} - 3840 q^{84} - 3312 q^{85} + 3792 q^{87} - 12976 q^{90} + 7488 q^{92} + 10152 q^{93} + 7080 q^{95} - 432 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)