Properties

Label 322.2.i
Level $322$
Weight $2$
Character orbit 322.i
Rep. character $\chi_{322}(29,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $120$
Newform subspaces $5$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 520 120 400
Cusp forms 440 120 320
Eisenstein series 80 0 80

Trace form

\( 120q + 8q^{3} - 12q^{4} + 8q^{5} - 4q^{9} + O(q^{10}) \) \( 120q + 8q^{3} - 12q^{4} + 8q^{5} - 4q^{9} + 12q^{11} + 8q^{12} + 24q^{13} + 4q^{14} - 4q^{15} - 12q^{16} - 28q^{17} - 36q^{18} - 20q^{19} + 8q^{20} + 4q^{21} - 32q^{22} - 20q^{23} - 36q^{26} + 56q^{27} - 4q^{29} - 20q^{30} + 12q^{31} + 4q^{33} + 16q^{34} + 8q^{35} - 4q^{36} + 16q^{38} - 8q^{39} + 4q^{41} + 4q^{42} - 8q^{43} + 12q^{44} + 72q^{45} + 20q^{46} - 24q^{47} + 8q^{48} - 12q^{49} + 16q^{50} + 20q^{51} + 24q^{52} + 16q^{53} + 24q^{54} - 96q^{55} + 4q^{56} - 88q^{57} + 32q^{58} - 104q^{59} - 4q^{60} + 32q^{61} - 92q^{62} + 24q^{63} - 12q^{64} + 48q^{65} - 112q^{66} - 12q^{67} + 16q^{68} - 124q^{69} + 8q^{70} - 124q^{71} + 8q^{72} - 8q^{73} - 124q^{74} + 84q^{75} + 24q^{76} - 52q^{78} + 52q^{79} - 36q^{80} - 80q^{81} + 24q^{82} - 96q^{83} + 4q^{84} - 24q^{85} + 36q^{86} + 72q^{87} + 12q^{88} + 52q^{89} + 112q^{90} - 32q^{91} + 24q^{92} + 88q^{93} + 16q^{94} + 84q^{95} - 64q^{97} + 156q^{99} + O(q^{100}) \)

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.i.a \(10\) \(2.571\) \(\Q(\zeta_{22})\) None \(1\) \(-3\) \(5\) \(1\) \(q-\zeta_{22}^{4}q^{2}+(-1-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
322.2.i.b \(10\) \(2.571\) \(\Q(\zeta_{22})\) None \(1\) \(5\) \(8\) \(1\) \(q-\zeta_{22}^{4}q^{2}+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
322.2.i.c \(20\) \(2.571\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(4\) \(-5\) \(-2\) \(q+\beta _{19}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
322.2.i.d \(40\) \(2.571\) None \(-4\) \(0\) \(9\) \(4\)
322.2.i.e \(40\) \(2.571\) None \(4\) \(2\) \(-9\) \(-4\)

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

\( S_{2}^{\mathrm{old}}(322, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)