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

\( 320q + 16q^{4} - 20q^{9} + O(q^{10}) \) \( 320q + 16q^{4} - 20q^{9} + 16q^{16} + 44q^{18} - 132q^{21} - 48q^{23} - 12q^{24} + 40q^{25} + 12q^{26} - 44q^{28} - 44q^{30} + 12q^{31} - 26q^{35} + 40q^{36} + 44q^{37} - 20q^{39} - 88q^{43} + 12q^{46} - 24q^{47} + 10q^{49} + 44q^{51} - 72q^{54} - 22q^{56} - 88q^{57} - 28q^{58} - 72q^{59} - 110q^{63} - 32q^{64} - 154q^{65} - 44q^{70} + 64q^{71} - 44q^{72} + 96q^{75} - 102q^{77} + 48q^{78} - 88q^{79} + 12q^{81} - 48q^{82} - 22q^{84} - 60q^{85} - 22q^{86} - 294q^{87} + 8q^{92} + 64q^{93} + 36q^{94} - 22q^{95} + 12q^{96} - 12q^{98} - 88q^{99} + O(q^{100}) \)

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.o.a \(160\) \(2.571\) None \(-8\) \(6\) \(0\) \(-11\)
322.2.o.b \(160\) \(2.571\) None \(8\) \(-6\) \(0\) \(11\)

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

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