↑

Properties

Label 2475.2.bd
Level $2475$
Weight $2$
Character orbit 2475.bd
Rep. character $\chi_{2475}(379,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $592$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.bd (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

\( 592 q - 590 q^{4} + 6 q^{5} - 5 q^{7} + O(q^{10}) \) \( 592 q - 590 q^{4} + 6 q^{5} - 5 q^{7} - 4 q^{10} + q^{11} - 5 q^{13} - q^{14} + 550 q^{16} - 46 q^{19} + 7 q^{20} - 15 q^{22} + 10 q^{23} - 30 q^{25} - q^{26} - 35 q^{28} + 54 q^{29} - 9 q^{31} - 4 q^{34} + 8 q^{35} + 30 q^{37} + 2 q^{40} + 5 q^{41} + 31 q^{44} - q^{46} + 10 q^{47} + 135 q^{49} + 60 q^{50} - 15 q^{52} + 55 q^{53} - 13 q^{55} + q^{56} + 11 q^{59} - 16 q^{61} - 20 q^{62} - 530 q^{64} + 10 q^{65} + 25 q^{67} + 85 q^{68} + 103 q^{70} - 21 q^{71} + 10 q^{73} - 27 q^{74} + 114 q^{76} + 10 q^{77} + 15 q^{79} + 144 q^{80} + 80 q^{82} + 5 q^{83} - 40 q^{85} - 50 q^{86} + 75 q^{88} - 4 q^{89} - 10 q^{91} + 30 q^{92} + 37 q^{94} + 84 q^{95} - 60 q^{97} - 40 q^{98} + O(q^{100}) \)

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

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