Properties

Label 1950.2.l
Level $1950$
Weight $2$
Character orbit 1950.l
Rep. character $\chi_{1950}(443,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 888 144 744
Cusp forms 792 144 648
Eisenstein series 96 0 96

Trace form

\( 144 q - 8 q^{3} - 16 q^{6} - 8 q^{7} + O(q^{10}) \) \( 144 q - 8 q^{3} - 16 q^{6} - 8 q^{7} + 8 q^{12} - 144 q^{16} - 8 q^{22} - 20 q^{27} - 8 q^{28} + 8 q^{33} + 16 q^{36} + 64 q^{37} + 20 q^{42} + 64 q^{43} + 96 q^{46} + 8 q^{48} + 24 q^{51} - 8 q^{57} - 56 q^{58} - 128 q^{61} + 24 q^{63} - 56 q^{66} - 16 q^{67} - 24 q^{73} - 64 q^{81} + 32 q^{87} - 8 q^{88} + 32 q^{91} - 16 q^{93} + 16 q^{96} - 88 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)