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

\( 160 q - 16 q^{4} + 8 q^{9} + O(q^{10}) \) \( 160 q - 16 q^{4} + 8 q^{9} - 16 q^{16} - 20 q^{18} - 66 q^{21} + 36 q^{23} - 52 q^{25} - 22 q^{28} + 24 q^{29} + 44 q^{30} + 14 q^{35} + 8 q^{36} - 44 q^{37} - 16 q^{39} - 44 q^{43} + 50 q^{49} + 24 q^{50} - 44 q^{51} + 22 q^{56} - 44 q^{57} - 80 q^{58} + 110 q^{63} - 16 q^{64} - 308 q^{65} + 80 q^{70} - 16 q^{71} - 64 q^{72} + 126 q^{77} - 176 q^{79} + 36 q^{81} + 22 q^{84} + 60 q^{85} - 44 q^{86} - 8 q^{92} + 104 q^{93} + 64 q^{95} - 60 q^{98} + 88 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
322.2.k.a $80$ $2.571$ None \(-8\) \(0\) \(0\) \(-11\)
322.2.k.b $80$ $2.571$ None \(8\) \(0\) \(0\) \(11\)

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

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