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Properties

Label 2475.4.dp
Level $2475$
Weight $4$
Character orbit 2475.dp
Rep. character $\chi_{2475}(1063,\cdot)$
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.dp (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

\( 3584 q + 10 q^{2} - 10 q^{4} + 30 q^{5} + 30 q^{7} + 10 q^{8} + O(q^{10}) \) \( 3584 q + 10 q^{2} - 10 q^{4} + 30 q^{5} + 30 q^{7} + 10 q^{8} + 120 q^{10} + 6 q^{11} - 10 q^{13} + 10 q^{14} + 14142 q^{16} + 330 q^{17} - 130 q^{19} + 514 q^{20} + 1672 q^{22} + 244 q^{23} + 18 q^{25} + 12 q^{26} + 710 q^{28} + 10 q^{29} - 2 q^{31} - 290 q^{32} - 20 q^{34} + 10 q^{35} - 1014 q^{37} - 1508 q^{38} - 10 q^{40} + 10 q^{41} + 10 q^{44} - 10 q^{46} + 4310 q^{47} + 3300 q^{49} + 10 q^{50} - 10 q^{52} + 1442 q^{53} - 640 q^{55} - 116 q^{56} + 78 q^{58} - 2670 q^{59} + 90 q^{62} + 1790 q^{64} + 836 q^{67} - 2160 q^{68} - 1080 q^{70} - 1858 q^{71} + 7130 q^{73} + 5390 q^{74} + 3178 q^{77} + 830 q^{79} + 3842 q^{80} - 8990 q^{82} - 4690 q^{83} - 6850 q^{85} + 2 q^{86} - 1600 q^{88} + 20 q^{89} - 2 q^{91} - 1390 q^{92} - 9180 q^{94} + 1130 q^{95} + 3450 q^{97} - 6560 q^{98} + O(q^{100}) \)

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

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