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Properties

Label 1088.2.s
Level $1088$
Weight $2$
Character orbit 1088.s
Rep. character $\chi_{1088}(625,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $68$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1088.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1088, [\chi])\).

Total New Old
Modular forms 304 76 228
Cusp forms 272 68 204
Eisenstein series 32 8 24

Trace form

\( 68 q + 4 q^{3} + 60 q^{9} + O(q^{10}) \) \( 68 q + 4 q^{3} + 60 q^{9} + 4 q^{11} - 4 q^{13} - 4 q^{17} - 4 q^{21} - 52 q^{25} + 16 q^{27} - 4 q^{29} + 4 q^{31} - 8 q^{33} + 4 q^{35} + 12 q^{39} + 48 q^{47} - 4 q^{51} - 12 q^{57} + 32 q^{59} + 32 q^{63} + 4 q^{65} + 4 q^{67} + 28 q^{69} + 8 q^{73} - 4 q^{75} - 28 q^{77} - 12 q^{79} + 28 q^{81} + 24 q^{85} - 24 q^{87} - 40 q^{91} - 12 q^{93} + 4 q^{95} - 4 q^{97} + 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1088, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1088.2.s.a 1088.s 272.s $68$ $8.688$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1088, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 2}\)