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Properties

Label 2475.4.dd
Level $2475$
Weight $4$
Character orbit 2475.dd
Rep. character $\chi_{2475}(28,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $3584$
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.dd (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8704 3616 5088
Cusp forms 8576 3584 4992
Eisenstein series 128 32 96

Trace form

\( 3584 q + 10 q^{2} - 10 q^{5} - 10 q^{7} - 70 q^{8} + O(q^{10}) \) \( 3584 q + 10 q^{2} - 10 q^{5} - 10 q^{7} - 70 q^{8} - 120 q^{10} + 6 q^{11} - 250 q^{13} + 10 q^{14} - 56588 q^{16} + 330 q^{17} - 20 q^{19} - 126 q^{20} + 22 q^{22} + 244 q^{23} + 218 q^{25} + 12 q^{26} + 310 q^{28} + 20 q^{29} - 2 q^{31} + 290 q^{32} - 20 q^{34} + 1030 q^{35} + 906 q^{37} + 1042 q^{38} + 630 q^{40} + 10 q^{41} - 630 q^{44} - 10 q^{46} - 850 q^{47} - 3300 q^{49} + 1130 q^{50} + 4470 q^{52} + 182 q^{53} - 1430 q^{55} - 116 q^{56} - 2 q^{58} + 10 q^{59} - 10 q^{61} - 3470 q^{62} + 836 q^{67} - 630 q^{68} + 6430 q^{70} + 1242 q^{71} - 10 q^{73} - 5390 q^{74} + 1198 q^{77} + 830 q^{79} + 5852 q^{80} - 4250 q^{82} + 6710 q^{83} + 5050 q^{85} + 12 q^{86} - 8370 q^{88} + 20 q^{89} - 2 q^{91} + 10940 q^{92} + 5510 q^{94} + 1260 q^{95} + 3510 q^{97} + 6560 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)