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Properties

Label 1900.2.co
Level $1900$
Weight $2$
Character orbit 1900.co
Rep. character $\chi_{1900}(9,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $1200$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.co (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 7344 1200 6144
Cusp forms 7056 1200 5856
Eisenstein series 288 0 288

Trace form

\( 1200 q + O(q^{10}) \) \( 1200 q - 9 q^{11} + 27 q^{15} + 30 q^{23} + 66 q^{25} + 18 q^{29} + 30 q^{33} + 21 q^{35} - 48 q^{45} - 60 q^{47} + 570 q^{49} - 60 q^{51} - 36 q^{59} + 72 q^{61} - 60 q^{65} + 48 q^{69} + 114 q^{71} + 24 q^{79} + 48 q^{81} - 30 q^{83} + 42 q^{85} + 60 q^{87} + 36 q^{89} + 21 q^{95} + 90 q^{97} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)