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Properties

Label 1456.2.w
Level $1456$
Weight $2$
Character orbit 1456.w
Rep. character $\chi_{1456}(993,\cdot)$
Character field $\Q(\zeta_{4})$
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.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
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

\( 108 q - 2 q^{7} - 108 q^{9} + O(q^{10}) \) \( 108 q - 2 q^{7} - 108 q^{9} + 4 q^{11} - 8 q^{15} + 4 q^{21} - 8 q^{29} + 4 q^{35} - 4 q^{37} + 24 q^{39} - 24 q^{53} - 24 q^{57} + 26 q^{63} - 20 q^{65} + 12 q^{67} + 12 q^{71} + 8 q^{79} + 92 q^{81} - 24 q^{85} - 22 q^{91} - 24 q^{93} + 52 q^{99} + O(q^{100}) \)

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

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