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Properties

Label 728.2.dl
Level $728$
Weight $2$
Character orbit 728.dl
Rep. character $\chi_{728}(33,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 728.dl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(728, [\chi])\).

Total New Old
Modular forms 480 112 368
Cusp forms 416 112 304
Eisenstein series 64 0 64

Trace form

\( 112 q - 4 q^{7} - 112 q^{9} + O(q^{10}) \) \( 112 q - 4 q^{7} - 112 q^{9} - 4 q^{11} + 8 q^{15} + 12 q^{19} - 12 q^{21} - 4 q^{29} + 48 q^{31} + 24 q^{33} - 20 q^{35} - 4 q^{37} - 44 q^{39} - 36 q^{41} - 48 q^{43} - 36 q^{47} - 24 q^{51} - 4 q^{53} + 16 q^{57} + 12 q^{63} + 12 q^{65} - 28 q^{67} - 56 q^{71} + 60 q^{73} + 144 q^{81} - 24 q^{83} - 16 q^{85} + 48 q^{87} - 48 q^{91} - 64 q^{93} + 24 q^{95} + 36 q^{97} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(728, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
728.2.dl.a 728.dl 91.w $112$ $5.813$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(728, [\chi])\) into lower level spaces

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