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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
322.2.i.a 322.i 23.c $10$ $2.571$ \(\Q(\zeta_{22})\) None \(1\) \(-3\) \(5\) \(1\) $\mathrm{SU}(2)[C_{11}]$ \(q-\zeta_{22}^{4}q^{2}+(-1-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
322.2.i.b 322.i 23.c $10$ $2.571$ \(\Q(\zeta_{22})\) None \(1\) \(5\) \(8\) \(1\) $\mathrm{SU}(2)[C_{11}]$ \(q-\zeta_{22}^{4}q^{2}+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
322.2.i.c 322.i 23.c $20$ $2.571$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(4\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{11}]$ \(q+\beta _{19}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
322.2.i.d 322.i 23.c $40$ $2.571$ None \(-4\) \(0\) \(9\) \(4\) $\mathrm{SU}(2)[C_{11}]$
322.2.i.e 322.i 23.c $40$ $2.571$ None \(4\) \(2\) \(-9\) \(-4\) $\mathrm{SU}(2)[C_{11}]$

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

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