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Properties

Label 352.2.s
Level $352$
Weight $2$
Character orbit 352.s
Rep. character $\chi_{352}(79,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $40$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 352 = 2^{5} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 352.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

Total New Old
Modular forms 224 56 168
Cusp forms 160 40 120
Eisenstein series 64 16 48

Trace form

\( 40 q + 6 q^{3} - 12 q^{9} + 12 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{25} - 6 q^{27} - 6 q^{33} + 10 q^{35} - 10 q^{41} - 4 q^{49} + 10 q^{51} - 10 q^{57} - 10 q^{59} + 56 q^{67} - 10 q^{73} - 34 q^{75}+ \cdots - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
352.2.s.a 352.s 88.k $8$ $2.811$ 8.0.64000000.1 \(\Q(\sqrt{-2}) \) 88.2.k.a \(0\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(1+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
352.2.s.b 352.s 88.k $32$ $2.811$ None 88.2.k.b \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)