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Properties

Label 2475.2.s
Level $2475$
Weight $2$
Character orbit 2475.s
Rep. character $\chi_{2475}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $592$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.s (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 1472 608 864
Cusp forms 1408 592 816
Eisenstein series 64 16 48

Trace form

\( 592 q + 6 q^{2} + 578 q^{4} + 4 q^{5} - 5 q^{7} + 18 q^{8} + O(q^{10}) \) \( 592 q + 6 q^{2} + 578 q^{4} + 4 q^{5} - 5 q^{7} + 18 q^{8} - 16 q^{10} + 5 q^{11} + 11 q^{13} + 3 q^{14} + 574 q^{16} - 46 q^{19} + 35 q^{20} - 19 q^{22} + 20 q^{23} + 18 q^{25} + 13 q^{26} - 35 q^{28} + 54 q^{29} + 7 q^{31} + 22 q^{32} - 8 q^{34} - 16 q^{35} + 6 q^{37} + 22 q^{38} - 28 q^{40} - 3 q^{41} - 52 q^{43} + 43 q^{44} - q^{46} - 20 q^{47} - 137 q^{49} + 30 q^{50} + 25 q^{52} + 23 q^{53} - 9 q^{55} + 19 q^{56} + 2 q^{58} + 11 q^{59} + 14 q^{61} - 42 q^{62} + 518 q^{64} + 58 q^{65} - 43 q^{67} + 25 q^{68} - 45 q^{70} + 3 q^{71} - 24 q^{73} - 23 q^{74} - 194 q^{76} + 15 q^{79} + 116 q^{80} - 34 q^{82} - 71 q^{83} - 82 q^{85} + 62 q^{86} - 29 q^{88} - 24 q^{89} + 8 q^{91} + 178 q^{92} + 33 q^{94} - 44 q^{95} - 48 q^{97} + 72 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

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