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Properties

Label 1925.2.ga
Level $1925$
Weight $2$
Character orbit 1925.ga
Rep. character $\chi_{1925}(82,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1925.ga (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1925, [\chi])\).

Total New Old
Modular forms 4032 2368 1664
Cusp forms 3648 2240 1408
Eisenstein series 384 128 256

Trace form

\( 2240 q + 6 q^{2} + 18 q^{3} + 10 q^{7} + 8 q^{8} + O(q^{10}) \) \( 2240 q + 6 q^{2} + 18 q^{3} + 10 q^{7} + 8 q^{8} + 72 q^{12} - 252 q^{16} + 18 q^{17} + 2 q^{18} - 64 q^{21} + 48 q^{22} + 32 q^{23} - 84 q^{26} - 80 q^{28} - 36 q^{31} + 48 q^{32} + 180 q^{33} + 368 q^{36} + 10 q^{37} + 18 q^{38} + 16 q^{42} + 104 q^{43} + 8 q^{46} + 6 q^{47} + 52 q^{51} - 30 q^{52} + 26 q^{53} + 176 q^{56} + 112 q^{57} - 58 q^{58} - 36 q^{61} - 112 q^{63} - 264 q^{66} + 64 q^{67} - 78 q^{68} + 144 q^{71} - 14 q^{72} + 78 q^{73} - 80 q^{77} + 312 q^{78} - 156 q^{81} + 90 q^{82} - 52 q^{86} + 60 q^{87} + 26 q^{88} - 16 q^{91} + 8 q^{92} - 122 q^{93} - 684 q^{96} + 344 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1925, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)