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Properties

Label 1456.2.co
Level $1456$
Weight $2$
Character orbit 1456.co
Rep. character $\chi_{1456}(753,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.co (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

\( 108 q - 2 q^{3} - 52 q^{9} + O(q^{10}) \) \( 108 q - 2 q^{3} - 52 q^{9} - 4 q^{13} - 2 q^{17} + 2 q^{23} + 44 q^{25} + 28 q^{27} - 8 q^{29} + 14 q^{35} + 14 q^{39} + 40 q^{43} - 12 q^{49} - 34 q^{51} + 2 q^{53} - 4 q^{55} + 2 q^{61} + 16 q^{65} + 36 q^{69} + 8 q^{75} + 18 q^{77} + 30 q^{79} - 30 q^{81} + 32 q^{87} + 4 q^{91} + 10 q^{95} + O(q^{100}) \)

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

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