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Properties

Label 2475.2.dq
Level $2475$
Weight $2$
Character orbit 2475.dq
Rep. character $\chi_{2475}(172,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1184$
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.dq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2944 1216 1728
Cusp forms 2816 1184 1632
Eisenstein series 128 32 96

Trace form

\( 1184 q + 10 q^{2} - 10 q^{4} + 10 q^{5} - 10 q^{7} + 10 q^{8} + O(q^{10}) \) \( 1184 q + 10 q^{2} - 10 q^{4} + 10 q^{5} - 10 q^{7} + 10 q^{8} - 40 q^{10} + 6 q^{11} - 30 q^{13} + 10 q^{14} + 282 q^{16} + 20 q^{17} + 10 q^{19} + 4 q^{20} - 34 q^{22} + 42 q^{23} + 8 q^{25} + 12 q^{26} - 30 q^{28} + 10 q^{29} - 12 q^{31} - 20 q^{34} + 10 q^{35} - 40 q^{37} + 14 q^{38} - 10 q^{40} - 70 q^{43} + 50 q^{44} - 10 q^{46} - 12 q^{47} - 60 q^{49} + 130 q^{50} + 30 q^{52} + 68 q^{53} + 4 q^{56} - 74 q^{58} - 20 q^{59} - 10 q^{61} + 100 q^{62} + 70 q^{64} + 20 q^{65} + 70 q^{67} - 60 q^{68} + 10 q^{70} - 8 q^{71} + 20 q^{73} - 110 q^{74} - 186 q^{77} - 10 q^{79} + 232 q^{80} - 70 q^{82} + 10 q^{83} + 30 q^{85} + 2 q^{86} - 50 q^{88} + 70 q^{89} - 12 q^{91} - 102 q^{92} + 140 q^{94} + 80 q^{95} - 38 q^{97} + 70 q^{98} + O(q^{100}) \)

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

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