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Properties

Label 1950.2.by
Level $1950$
Weight $2$
Character orbit 1950.by
Rep. character $\chi_{1950}(73,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $560$
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.by (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 3424 560 2864
Cusp forms 3296 560 2736
Eisenstein series 128 0 128

Trace form

\( 560 q - 4 q^{2} - 140 q^{4} - 4 q^{8} + O(q^{10}) \) \( 560 q - 4 q^{2} - 140 q^{4} - 4 q^{8} - 8 q^{13} - 8 q^{15} - 140 q^{16} + 4 q^{17} + 40 q^{19} - 16 q^{23} + 12 q^{25} - 80 q^{29} + 16 q^{32} + 24 q^{33} + 20 q^{34} + 20 q^{37} - 140 q^{41} + 32 q^{43} - 4 q^{45} - 560 q^{49} + 20 q^{50} - 8 q^{52} + 60 q^{53} + 32 q^{55} - 8 q^{60} - 140 q^{64} + 32 q^{65} + 48 q^{67} + 4 q^{68} - 56 q^{70} + 104 q^{73} + 48 q^{77} + 16 q^{78} + 140 q^{81} + 4 q^{82} - 4 q^{85} - 48 q^{87} - 40 q^{89} + 4 q^{90} + 120 q^{91} - 16 q^{92} - 128 q^{95} - 60 q^{98} + O(q^{100}) \)

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

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