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Properties

Label 2475.2.i
Level $2475$
Weight $2$
Character orbit 2475.i
Rep. character $\chi_{2475}(826,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $380$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 744 380 364
Cusp forms 696 380 316
Eisenstein series 48 0 48

Trace form

\( 380 q + q^{3} - 190 q^{4} - 14 q^{6} - 2 q^{7} - 12 q^{8} + 5 q^{9} + O(q^{10}) \) \( 380 q + q^{3} - 190 q^{4} - 14 q^{6} - 2 q^{7} - 12 q^{8} + 5 q^{9} + 4 q^{11} + 6 q^{12} - 2 q^{13} + 14 q^{14} - 190 q^{16} + 12 q^{17} - 36 q^{18} + 4 q^{19} + 4 q^{21} - 18 q^{23} + 70 q^{24} - 2 q^{27} + 16 q^{28} - 12 q^{29} - 11 q^{31} - 28 q^{32} - 2 q^{33} + 12 q^{34} + 2 q^{36} + 10 q^{37} + 26 q^{38} - 8 q^{39} - 12 q^{41} - 30 q^{42} - 8 q^{43} - 20 q^{44} - 22 q^{47} - 10 q^{48} - 204 q^{49} - 22 q^{51} + 10 q^{52} + 28 q^{53} + 32 q^{54} + 12 q^{56} + 62 q^{57} + 18 q^{58} + 51 q^{59} - 26 q^{61} - 12 q^{62} + 60 q^{63} + 320 q^{64} - 10 q^{66} - 17 q^{67} + 38 q^{68} - 15 q^{69} - 42 q^{71} + 84 q^{72} + 28 q^{73} + 26 q^{74} + 4 q^{76} - 8 q^{77} - 70 q^{78} - 2 q^{79} - 27 q^{81} - 84 q^{82} + 56 q^{83} - 98 q^{84} - 20 q^{86} + 8 q^{87} + 44 q^{89} + 44 q^{91} - 86 q^{92} - 77 q^{93} + 6 q^{94} - 100 q^{96} + 19 q^{97} - 172 q^{98} - 15 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)