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Properties

Label 1568.2.bg
Level $1568$
Weight $2$
Character orbit 1568.bg
Rep. character $\chi_{1568}(111,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $324$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.bg (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1568, [\chi])\).

Total New Old
Modular forms 1392 348 1044
Cusp forms 1296 324 972
Eisenstein series 96 24 72

Trace form

\( 324 q + 14 q^{3} + 40 q^{9} + O(q^{10}) \) \( 324 q + 14 q^{3} + 40 q^{9} + 10 q^{11} - 14 q^{17} - 56 q^{25} + 14 q^{27} - 14 q^{33} - 10 q^{35} - 14 q^{41} + 10 q^{43} - 20 q^{49} + 62 q^{51} + 4 q^{57} + 14 q^{59} + 10 q^{65} + 48 q^{67} - 14 q^{73} + 14 q^{75} - 100 q^{81} + 14 q^{83} - 14 q^{89} - 130 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)