Properties

Label 1456.2.t
Level $1456$
Weight $2$
Character orbit 1456.t
Rep. character $\chi_{1456}(81,\cdot)$
Character field $\Q(\zeta_{3})$
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.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 108 q - 6 q^{3} - 2 q^{5} + 5 q^{7} + 98 q^{9} + O(q^{10}) \) \( 108 q - 6 q^{3} - 2 q^{5} + 5 q^{7} + 98 q^{9} + 2 q^{11} - 4 q^{13} - q^{15} + q^{17} + 10 q^{19} - 7 q^{21} - q^{23} - 48 q^{25} - 18 q^{27} - 2 q^{29} + 10 q^{31} - 26 q^{33} + 6 q^{35} + q^{37} - 22 q^{39} + 6 q^{41} + 10 q^{43} - 15 q^{45} + 2 q^{47} + 11 q^{49} - 4 q^{51} + 2 q^{53} - 19 q^{55} - 14 q^{57} - 9 q^{59} - 10 q^{61} + 48 q^{63} - 22 q^{65} - 2 q^{67} - 16 q^{69} + 6 q^{71} + 2 q^{73} + 28 q^{75} - 31 q^{77} + 16 q^{79} + 52 q^{81} + 8 q^{83} + 3 q^{85} - 19 q^{87} + 9 q^{89} - 45 q^{91} - 13 q^{93} + 21 q^{95} - 10 q^{97} + 56 q^{99} + O(q^{100}) \)

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

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