↑

Properties

Label 1456.2.cr
Level $1456$
Weight $2$
Character orbit 1456.cr
Rep. character $\chi_{1456}(641,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.cr (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

Total New Old
Modular forms 472 116 356
Cusp forms 424 108 316
Eisenstein series 48 8 40

Trace form

\( 108 q - 5 q^{3} - 3 q^{7} - 49 q^{9} + O(q^{10}) \) \( 108 q - 5 q^{3} - 3 q^{7} - 49 q^{9} + 3 q^{11} - 4 q^{13} + 15 q^{15} - 2 q^{17} + 3 q^{19} + 9 q^{21} + 2 q^{23} + 44 q^{25} + 46 q^{27} - 2 q^{29} + 24 q^{31} - 3 q^{33} + 11 q^{35} + 5 q^{39} - 6 q^{41} + 10 q^{43} - 9 q^{49} + 20 q^{51} + 2 q^{53} + 23 q^{55} + 5 q^{61} + 27 q^{63} - 8 q^{65} - 3 q^{67} + 42 q^{71} + 12 q^{73} - 76 q^{75} - 9 q^{77} - 12 q^{79} - 42 q^{81} - 21 q^{85} - 58 q^{87} + 37 q^{91} + 46 q^{95} + 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)