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Properties

Label 1425.2.cs
Level $1425$
Weight $2$
Character orbit 1425.cs
Rep. character $\chi_{1425}(13,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $4800$
Sturm bound $400$

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Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.cs (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1425, [\chi])\).

Total New Old
Modular forms 9792 4800 4992
Cusp forms 9408 4800 4608
Eisenstein series 384 0 384

Trace form

\( 4800 q + 12 q^{7} + O(q^{10}) \) \( 4800 q + 12 q^{7} - 120 q^{20} + 96 q^{22} + 96 q^{23} + 24 q^{25} + 72 q^{28} - 120 q^{29} + 12 q^{32} - 48 q^{33} + 312 q^{38} - 168 q^{40} - 372 q^{43} - 264 q^{47} - 36 q^{53} + 24 q^{57} + 144 q^{58} - 240 q^{59} - 48 q^{60} - 432 q^{62} + 144 q^{67} + 48 q^{68} + 48 q^{70} + 72 q^{72} + 36 q^{73} + 216 q^{77} - 120 q^{78} - 24 q^{80} - 144 q^{82} - 228 q^{83} - 192 q^{85} - 192 q^{87} - 360 q^{88} + 144 q^{90} - 552 q^{92} - 24 q^{95} - 96 q^{97} - 192 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1425, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)