Properties

Label 1575.2.eg
Level $1575$
Weight $2$
Character orbit 1575.eg
Rep. character $\chi_{1575}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3776$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.eg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\( 3776 q - 16 q^{2} - 20 q^{4} - 8 q^{7} - 48 q^{8} - 40 q^{9} + O(q^{10}) \) \( 3776 q - 16 q^{2} - 20 q^{4} - 8 q^{7} - 48 q^{8} - 40 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} - 460 q^{16} - 32 q^{18} - 12 q^{21} - 32 q^{22} - 8 q^{23} - 16 q^{25} - 8 q^{28} - 20 q^{29} + 16 q^{30} - 68 q^{32} - 32 q^{35} + 8 q^{36} - 64 q^{37} - 58 q^{42} - 16 q^{43} - 80 q^{44} - 48 q^{46} + 56 q^{50} - 64 q^{51} - 144 q^{53} + 26 q^{56} - 88 q^{57} + 24 q^{58} - 200 q^{60} - 94 q^{63} - 80 q^{64} - 40 q^{65} - 16 q^{67} - 28 q^{70} - 48 q^{71} - 20 q^{72} + 44 q^{77} + 4 q^{78} - 20 q^{79} - 24 q^{81} - 140 q^{84} - 16 q^{85} - 12 q^{86} + 40 q^{88} - 24 q^{91} + 48 q^{92} - 128 q^{93} - 60 q^{95} + 40 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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