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Properties

Label 2475.4.n
Level $2475$
Weight $4$
Character orbit 2475.n
Rep. character $\chi_{2475}(361,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1792$
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.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4352 1808 2544
Cusp forms 4288 1792 2496
Eisenstein series 64 16 48

Trace form

\( 1792 q + q^{2} - 1785 q^{4} - 9 q^{5} - 4 q^{7} + 9 q^{8} + O(q^{10}) \) \( 1792 q + q^{2} - 1785 q^{4} - 9 q^{5} - 4 q^{7} + 9 q^{8} - 124 q^{10} + 31 q^{11} - 145 q^{13} + 9 q^{14} - 7045 q^{16} - 31 q^{17} - 141 q^{19} + 272 q^{20} + 63 q^{22} - 82 q^{23} - 125 q^{25} - 46 q^{26} - 342 q^{28} + 349 q^{29} + 786 q^{31} + 68 q^{32} - 14 q^{34} - 437 q^{35} - 697 q^{37} - 979 q^{38} + 1092 q^{40} - 2810 q^{41} - 1684 q^{43} + 361 q^{44} - 121 q^{46} - 2201 q^{47} - 21160 q^{49} - 2760 q^{50} + 2251 q^{52} + 487 q^{53} + 77 q^{55} - 1294 q^{56} + 2206 q^{58} - 229 q^{59} - 321 q^{61} - 941 q^{62} - 28965 q^{64} + 700 q^{65} - 580 q^{67} + 597 q^{68} + 3263 q^{70} + 354 q^{71} - 3870 q^{73} + 2033 q^{74} + 10484 q^{76} + 7374 q^{77} - 1245 q^{79} + 5354 q^{80} + 3534 q^{82} - 2175 q^{83} + 1875 q^{85} - 875 q^{86} - 3477 q^{88} + 766 q^{89} + 2830 q^{91} - 6060 q^{92} - 1838 q^{94} + 929 q^{95} - 175 q^{97} + 63 q^{98} + O(q^{100}) \)

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

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