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Properties

Label 322.2.k
Level $322$
Weight $2$
Character orbit 322.k
Rep. character $\chi_{322}(83,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $160$
Newform subspaces $2$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(322, [\chi])\).

Total New Old
Modular forms 520 160 360
Cusp forms 440 160 280
Eisenstein series 80 0 80

Trace form

\( 160 q - 16 q^{4} + 8 q^{9} - 16 q^{16} - 20 q^{18} - 66 q^{21} + 36 q^{23} - 52 q^{25} - 22 q^{28} + 24 q^{29} + 44 q^{30} + 14 q^{35} + 8 q^{36} - 44 q^{37} - 16 q^{39} - 44 q^{43} + 50 q^{49} + 24 q^{50}+ \cdots + 88 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(322, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
322.2.k.a 322.k 161.k $80$ $2.571$ None 322.2.k.a \(-8\) \(0\) \(0\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
322.2.k.b 322.k 161.k $80$ $2.571$ None 322.2.k.b \(8\) \(0\) \(0\) \(11\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)