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Properties

Label 2475.2.u
Level $2475$
Weight $2$
Character orbit 2475.u
Rep. character $\chi_{2475}(626,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $444$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 744 468 276
Cusp forms 696 444 252
Eisenstein series 48 24 24

Trace form

\( 444 q + 3 q^{3} - 214 q^{4} + q^{9} + O(q^{10}) \) \( 444 q + 3 q^{3} - 214 q^{4} + q^{9} - 6 q^{11} + 10 q^{12} + 6 q^{14} - 206 q^{16} + 24 q^{23} - 6 q^{27} - 9 q^{31} - 16 q^{33} - 4 q^{34} + 82 q^{36} + 14 q^{37} - 18 q^{38} + 46 q^{42} - 6 q^{47} + 30 q^{48} + 188 q^{49} + 96 q^{56} + 6 q^{58} + 51 q^{59} + 376 q^{64} - 6 q^{66} - 7 q^{67} + 19 q^{69} - 18 q^{77} + 22 q^{78} + 9 q^{81} + 12 q^{82} - 120 q^{86} + 24 q^{88} - 20 q^{91} - 222 q^{92} - 45 q^{93} + 23 q^{97} - 57 q^{99} + O(q^{100}) \)

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

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