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Properties

Label 2475.2.cd
Level $2475$
Weight $2$
Character orbit 2475.cd
Rep. character $\chi_{2475}(289,\cdot)$
Character field $\Q(\zeta_{10})$
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.cd (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 592 q + 5 q^{2} + 145 q^{4} + q^{5} + 5 q^{7} + 5 q^{8} + O(q^{10}) \) \( 592 q + 5 q^{2} + 145 q^{4} + q^{5} + 5 q^{7} + 5 q^{8} - 4 q^{10} + 6 q^{11} + 9 q^{14} - 155 q^{16} + 9 q^{19} + 17 q^{20} - 10 q^{22} + 10 q^{23} + 15 q^{25} - q^{26} + 45 q^{28} - 11 q^{29} + 6 q^{31} - 4 q^{34} + 43 q^{35} - 40 q^{37} + 35 q^{38} + 7 q^{40} + 20 q^{41} + 21 q^{44} - q^{46} + 135 q^{49} + 30 q^{50} - 5 q^{52} - 10 q^{53} - 8 q^{55} + q^{56} + 30 q^{58} + q^{59} + 54 q^{61} - 90 q^{62} + 195 q^{64} + 10 q^{65} + 25 q^{67} - 85 q^{68} - 27 q^{70} + 4 q^{71} - 20 q^{73} - 27 q^{74} + 114 q^{76} - 40 q^{77} + 15 q^{79} + 9 q^{80} - 80 q^{82} + 55 q^{83} - 20 q^{85} - 15 q^{86} - 50 q^{88} - 4 q^{89} - 30 q^{91} + 42 q^{94} + 34 q^{95} - 5 q^{97} - 40 q^{98} + O(q^{100}) \)

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

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