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Properties

Label 322.2.o
Level $322$
Weight $2$
Character orbit 322.o
Rep. character $\chi_{322}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $320$
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.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{66})\)
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 1040 320 720
Cusp forms 880 320 560
Eisenstein series 160 0 160

Trace form

\( 320 q + 16 q^{4} - 20 q^{9} + 16 q^{16} + 44 q^{18} - 132 q^{21} - 48 q^{23} - 12 q^{24} + 40 q^{25} + 12 q^{26} - 44 q^{28} - 44 q^{30} + 12 q^{31} - 26 q^{35} + 40 q^{36} + 44 q^{37} - 20 q^{39} - 88 q^{43}+ \cdots - 88 q^{99}+O(q^{100}) \) 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.o.a 322.o 161.o $160$ $2.571$ None 322.2.o.a \(-8\) \(6\) \(0\) \(-11\) $\mathrm{SU}(2)[C_{66}]$
322.2.o.b 322.o 161.o $160$ $2.571$ None 322.2.o.b \(8\) \(-6\) \(0\) \(11\) $\mathrm{SU}(2)[C_{66}]$

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

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