Properties

Label 1425.2.bp
Level $1425$
Weight $2$
Character orbit 1425.bp
Rep. character $\chi_{1425}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $800$
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.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(400\)

Dimensions

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

Total New Old
Modular forms 1632 800 832
Cusp forms 1568 800 768
Eisenstein series 64 0 64

Trace form

\( 800q + 4q^{5} - 4q^{7} + O(q^{10}) \) \( 800q + 4q^{5} - 4q^{7} + 200q^{16} + 16q^{17} - 20q^{19} + 40q^{20} - 48q^{23} - 20q^{25} + 8q^{28} + 64q^{30} - 64q^{35} - 200q^{36} - 36q^{38} - 124q^{43} + 280q^{44} + 172q^{47} - 80q^{55} + 176q^{58} - 192q^{62} + 4q^{63} - 120q^{64} + 40q^{68} + 4q^{73} + 68q^{77} - 168q^{80} + 200q^{81} + 72q^{82} - 48q^{83} + 88q^{85} - 128q^{87} + 256q^{92} + 192q^{93} - 196q^{95} + 40q^{96} + O(q^{100}) \)

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

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