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Properties

Label 1925.2.gd
Level $1925$
Weight $2$
Character orbit 1925.gd
Rep. character $\chi_{1925}(18,\cdot)$
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.gd (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

\( 2240 q + 10 q^{2} + 6 q^{3} - 80 q^{6} + 30 q^{7} + 40 q^{8} + O(q^{10}) \) \( 2240 q + 10 q^{2} + 6 q^{3} - 80 q^{6} + 30 q^{7} + 40 q^{8} - 16 q^{11} + 40 q^{13} - 284 q^{16} + 30 q^{17} + 10 q^{18} + 32 q^{23} + 36 q^{26} + 80 q^{28} - 12 q^{31} - 32 q^{33} + 368 q^{36} + 34 q^{37} + 22 q^{38} + 160 q^{41} + 80 q^{42} - 80 q^{46} - 34 q^{47} + 208 q^{48} + 220 q^{51} + 10 q^{52} - 14 q^{53} - 496 q^{56} + 200 q^{57} + 70 q^{58} - 180 q^{61} + 40 q^{62} - 104 q^{66} - 32 q^{67} - 90 q^{68} - 240 q^{71} + 70 q^{72} + 130 q^{73} + 140 q^{77} + 8 q^{78} - 156 q^{81} - 2 q^{82} + 40 q^{83} - 52 q^{86} + 54 q^{88} + 64 q^{91} + 136 q^{92} + 70 q^{93} + 260 q^{96} + 64 q^{97} + O(q^{100}) \)

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

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