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Properties

Label 2475.4.ft
Level $2475$
Weight $4$
Character orbit 2475.ft
Rep. character $\chi_{2475}(142,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $17216$
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.ft (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
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 17344 0
Cusp forms 17216 17216 0
Eisenstein series 128 128 0

Trace form

\( 17216 q - 28 q^{3} - 20 q^{4} - 16 q^{5} - 40 q^{9} + O(q^{10}) \) \( 17216 q - 28 q^{3} - 20 q^{4} - 16 q^{5} - 40 q^{9} - 6 q^{11} + 44 q^{12} - 20 q^{14} - 40 q^{15} - 34060 q^{16} + 624 q^{20} + 24 q^{22} + 216 q^{23} - 592 q^{25} - 128 q^{26} + 560 q^{27} - 12 q^{31} - 186 q^{33} - 20 q^{34} + 488 q^{36} + 80 q^{37} + 64 q^{38} - 1460 q^{42} - 40 q^{44} - 3244 q^{45} + 760 q^{47} - 204 q^{48} + 1496 q^{53} - 532 q^{55} + 1012 q^{56} + 928 q^{58} - 1680 q^{59} + 6388 q^{60} - 80 q^{64} + 852 q^{66} + 596 q^{67} - 40 q^{69} + 984 q^{70} + 2432 q^{71} + 10888 q^{75} + 4644 q^{77} + 7024 q^{78} - 312 q^{80} + 616 q^{81} - 12 q^{86} - 2848 q^{88} - 27280 q^{89} - 48 q^{91} + 21620 q^{92} - 8972 q^{93} - 1168 q^{97} + O(q^{100}) \)

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.