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Properties

Label 1456.2.hm
Level $1456$
Weight $2$
Character orbit 1456.hm
Rep. character $\chi_{1456}(145,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $216$
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.hm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 944 232 712
Cusp forms 848 216 632
Eisenstein series 96 16 80

Trace form

\( 216 q + 6 q^{3} - 6 q^{5} - 4 q^{7} + 102 q^{9} + O(q^{10}) \) \( 216 q + 6 q^{3} - 6 q^{5} - 4 q^{7} + 102 q^{9} + 2 q^{11} + 2 q^{15} - 12 q^{17} + 18 q^{19} - 10 q^{21} - 4 q^{29} + 6 q^{31} - 6 q^{33} + 2 q^{35} - 2 q^{37} - 6 q^{39} + 24 q^{41} + 60 q^{43} - 6 q^{45} + 6 q^{47} - 30 q^{49} + 36 q^{51} - 12 q^{53} + 30 q^{57} - 42 q^{59} - 30 q^{61} - 20 q^{63} - 10 q^{65} + 6 q^{67} + 48 q^{71} - 6 q^{73} + 12 q^{75} + 4 q^{79} - 80 q^{81} - 18 q^{85} - 6 q^{89} - 92 q^{91} - 30 q^{93} - 4 q^{99} + O(q^{100}) \)

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

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