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Properties

Label 1925.2.fz
Level $1925$
Weight $2$
Character orbit 1925.fz
Rep. character $\chi_{1925}(12,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3200$
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.fz (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 3904 3200 704
Cusp forms 3776 3200 576
Eisenstein series 128 0 128

Trace form

\( 3200 q + 24 q^{8} + O(q^{10}) \) \( 3200 q + 24 q^{8} - 24 q^{15} - 400 q^{16} + 36 q^{17} + 16 q^{18} + 48 q^{23} + 76 q^{28} - 80 q^{29} + 16 q^{30} - 64 q^{32} + 12 q^{35} + 800 q^{36} - 192 q^{38} - 80 q^{39} + 48 q^{40} - 88 q^{42} + 112 q^{43} - 36 q^{45} + 72 q^{47} + 368 q^{50} - 432 q^{52} - 136 q^{53} + 120 q^{57} - 24 q^{58} - 240 q^{59} - 248 q^{60} + 104 q^{63} + 120 q^{64} - 48 q^{65} + 8 q^{67} - 576 q^{68} - 52 q^{70} - 52 q^{72} - 96 q^{73} - 48 q^{75} + 72 q^{78} - 108 q^{80} - 400 q^{81} - 312 q^{82} - 80 q^{84} - 48 q^{85} + 36 q^{87} + 96 q^{88} + 40 q^{92} + 20 q^{93} + 152 q^{95} - 48 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)