↑

Properties

Label 1568.2.bj
Level $1568$
Weight $2$
Character orbit 1568.bj
Rep. character $\chi_{1568}(113,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $324$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.bj (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

\( 324 q + 12 q^{7} + 40 q^{9} + O(q^{10}) \) \( 324 q + 12 q^{7} + 40 q^{9} + 22 q^{15} - 10 q^{17} + 10 q^{23} + 36 q^{25} + 96 q^{31} - 22 q^{33} + 22 q^{39} - 10 q^{41} + 14 q^{47} - 20 q^{49} + 46 q^{55} + 36 q^{57} + 24 q^{63} - 30 q^{65} + 90 q^{71} + 6 q^{73} + 24 q^{79} - 20 q^{81} + 46 q^{87} + 6 q^{89} - 64 q^{95} - 24 q^{97} + O(q^{100}) \)

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

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