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Properties

Label 1950.2.cj
Level $1950$
Weight $2$
Character orbit 1950.cj
Rep. character $\chi_{1950}(439,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $544$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.cj (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

Total New Old
Modular forms 3424 544 2880
Cusp forms 3296 544 2752
Eisenstein series 128 0 128

Trace form

\( 544 q + 68 q^{4} - 68 q^{9} + O(q^{10}) \) \( 544 q + 68 q^{4} - 68 q^{9} - 2 q^{10} - 12 q^{15} + 68 q^{16} + 24 q^{20} - 40 q^{23} - 20 q^{25} + 12 q^{26} + 12 q^{29} + 60 q^{33} - 4 q^{35} - 68 q^{36} - 30 q^{37} + 4 q^{40} - 144 q^{41} + 6 q^{45} - 208 q^{49} + 30 q^{50} + 64 q^{51} - 20 q^{53} - 40 q^{55} + 72 q^{59} - 36 q^{61} + 60 q^{62} - 136 q^{64} + 48 q^{65} + 32 q^{66} - 24 q^{69} + 28 q^{74} - 8 q^{75} - 160 q^{77} + 32 q^{79} + 6 q^{80} + 68 q^{81} - 66 q^{85} + 20 q^{87} - 4 q^{90} - 80 q^{91} + 16 q^{94} + 24 q^{95} - 240 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)