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Properties

Label 1425.2.cn
Level $1425$
Weight $2$
Character orbit 1425.cn
Rep. character $\chi_{1425}(4,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $2400$
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.cn (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(400\)

Dimensions

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

Total New Old
Modular forms 4896 2400 2496
Cusp forms 4704 2400 2304
Eisenstein series 192 0 192

Trace form

\( 2400 q + O(q^{10}) \) \( 2400 q - 18 q^{10} + 18 q^{11} + 36 q^{14} + 12 q^{15} + 108 q^{20} - 60 q^{22} - 60 q^{23} - 48 q^{25} - 36 q^{29} - 72 q^{31} - 30 q^{33} + 36 q^{35} - 90 q^{38} - 6 q^{45} - 84 q^{46} - 120 q^{47} + 1212 q^{49} + 18 q^{50} + 72 q^{55} + 360 q^{58} - 72 q^{59} + 24 q^{60} - 72 q^{61} + 300 q^{62} - 300 q^{64} + 48 q^{69} - 108 q^{70} + 24 q^{71} - 180 q^{72} - 48 q^{79} - 54 q^{80} - 120 q^{83} + 72 q^{84} - 162 q^{85} + 180 q^{86} + 120 q^{87} - 72 q^{89} - 72 q^{90} - 300 q^{92} - 24 q^{94} + 210 q^{95} - 180 q^{97} - 480 q^{98} + O(q^{100}) \)

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

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