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Properties

Label 1950.2.cm
Level $1950$
Weight $2$
Character orbit 1950.cm
Rep. character $\chi_{1950}(121,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $576$
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.cm (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 576 2848
Cusp forms 3296 576 2720
Eisenstein series 128 0 128

Trace form

\( 576 q - 72 q^{4} + 72 q^{9} + O(q^{10}) \) \( 576 q - 72 q^{4} + 72 q^{9} + 16 q^{13} + 12 q^{15} + 72 q^{16} - 24 q^{23} + 16 q^{25} + 8 q^{26} + 32 q^{29} + 36 q^{33} - 20 q^{35} - 72 q^{36} + 84 q^{41} + 8 q^{43} + 352 q^{49} - 24 q^{50} - 64 q^{51} + 8 q^{52} - 144 q^{53} + 72 q^{55} + 48 q^{58} + 72 q^{59} + 16 q^{61} - 36 q^{62} + 144 q^{64} + 28 q^{65} - 32 q^{66} + 72 q^{67} - 24 q^{69} + 8 q^{74} - 8 q^{75} + 240 q^{77} + 16 q^{78} + 32 q^{79} + 72 q^{81} - 64 q^{82} - 36 q^{85} + 36 q^{87} + 80 q^{91} + 32 q^{92} + 16 q^{94} - 120 q^{95} + 144 q^{98} + O(q^{100}) \)

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

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