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Properties

Label 2475.2.n
Level $2475$
Weight $2$
Character orbit 2475.n
Rep. character $\chi_{2475}(361,\cdot)$
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.n (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

\( 592 q + q^{2} - 147 q^{4} + 4 q^{5} + 3 q^{8} + O(q^{10}) \) \( 592 q + q^{2} - 147 q^{4} + 4 q^{5} + 3 q^{8} + 4 q^{10} + 5 q^{11} + 11 q^{13} + 3 q^{14} - 141 q^{16} + 9 q^{19} + q^{22} + 18 q^{25} + 18 q^{26} + 30 q^{28} - 11 q^{29} + 12 q^{31} + 12 q^{32} - 8 q^{34} + 24 q^{35} + q^{37} + 7 q^{38} - 28 q^{40} + 82 q^{41} + 18 q^{43} + 33 q^{44} + 19 q^{46} - 132 q^{49} - 50 q^{50} - 15 q^{52} + 58 q^{53} - 4 q^{55} - 16 q^{56} - 58 q^{58} - 4 q^{59} - 6 q^{61} + 13 q^{62} - 97 q^{64} - 32 q^{65} - 23 q^{67} - 35 q^{68} - 65 q^{70} + 28 q^{71} - 64 q^{73} - 23 q^{74} - 4 q^{76} - 115 q^{77} + 35 q^{79} + 46 q^{80} + 16 q^{82} - 21 q^{83} + 8 q^{85} + 47 q^{86} + 121 q^{88} + q^{89} + 18 q^{91} + 78 q^{92} + 8 q^{94} + 6 q^{95} + 52 q^{97} + 67 q^{98} + O(q^{100}) \)

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

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