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Properties

Label 1950.2.cq
Level $1950$
Weight $2$
Character orbit 1950.cq
Rep. character $\chi_{1950}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1120$
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.cq (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 6848 1120 5728
Cusp forms 6592 1120 5472
Eisenstein series 256 0 256

Trace form

\( 1120 q - 140 q^{4} - 4 q^{5} + O(q^{10}) \) \( 1120 q - 140 q^{4} - 4 q^{5} - 12 q^{13} - 8 q^{15} + 140 q^{16} - 8 q^{17} + 32 q^{18} - 40 q^{19} - 16 q^{20} - 16 q^{23} - 36 q^{25} + 80 q^{29} - 16 q^{33} + 40 q^{34} - 48 q^{37} + 260 q^{41} + 8 q^{43} + 48 q^{47} - 560 q^{49} - 32 q^{50} - 12 q^{53} - 272 q^{55} + 20 q^{58} + 8 q^{60} + 72 q^{62} + 280 q^{64} - 24 q^{65} + 72 q^{67} - 4 q^{68} + 96 q^{70} - 4 q^{72} - 160 q^{73} + 60 q^{74} + 48 q^{77} + 16 q^{78} + 8 q^{80} - 140 q^{81} + 196 q^{82} + 48 q^{83} - 104 q^{85} - 20 q^{89} + 4 q^{90} - 240 q^{91} - 32 q^{92} - 32 q^{95} - 144 q^{97} + 224 q^{98} + O(q^{100}) \)

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

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