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Properties

Label 1950.2.bt
Level $1950$
Weight $2$
Character orbit 1950.bt
Rep. character $\chi_{1950}(107,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $336$
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.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 1776 336 1440
Cusp forms 1584 336 1248
Eisenstein series 192 0 192

Trace form

\( 336 q + O(q^{10}) \) \( 336 q - 24 q^{13} + 168 q^{16} + 16 q^{18} + 32 q^{21} - 24 q^{27} - 52 q^{33} + 16 q^{36} + 8 q^{37} - 12 q^{42} + 8 q^{43} + 16 q^{46} + 160 q^{51} - 24 q^{52} + 96 q^{57} - 8 q^{58} - 48 q^{61} + 16 q^{63} + 64 q^{66} - 40 q^{67} + 8 q^{72} + 80 q^{73} + 8 q^{76} + 36 q^{78} - 16 q^{81} + 16 q^{82} + 8 q^{87} - 56 q^{91} + 68 q^{93} + 40 q^{97} + O(q^{100}) \)

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

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