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Properties

Label 2475.4.ec
Level $2475$
Weight $4$
Character orbit 2475.ec
Rep. character $\chi_{2475}(164,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $8608$
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.ec (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8672 8672 0
Cusp forms 8608 8608 0
Eisenstein series 64 64 0

Trace form

\( 8608 q - 20 q^{3} - 4294 q^{4} + 24 q^{5} - 44 q^{9} + O(q^{10}) \) \( 8608 q - 20 q^{3} - 4294 q^{4} + 24 q^{5} - 44 q^{9} - 9 q^{11} - 180 q^{12} - 18 q^{14} - 134 q^{15} + 16986 q^{16} - 168 q^{20} - 5 q^{22} - 30 q^{23} + 280 q^{25} - 20 q^{27} - 42 q^{31} + 790 q^{33} - 38 q^{34} - 1340 q^{36} - 40 q^{37} - 30 q^{38} + 2140 q^{42} + 4488 q^{45} - 30 q^{47} + 3260 q^{48} - 206208 q^{49} - 378 q^{55} + 6252 q^{56} - 10 q^{58} + 1476 q^{59} + 2610 q^{60} + 133512 q^{64} + 2778 q^{66} - 1540 q^{67} - 1760 q^{69} - 1980 q^{70} + 5744 q^{75} - 8175 q^{77} + 13800 q^{78} + 2100 q^{81} - 18 q^{86} - 5 q^{88} + 4092 q^{91} - 30 q^{92} - 10 q^{97} + 218 q^{99} + O(q^{100}) \)

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.