Space of modular forms of level 322, weight 2, and Character 322.i

• 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: $3$

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 + 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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
322.2.i.a	$322$	$2$	322.i	23.c	$11$	$10$	$1$	$2.571$	\(\Q(\zeta_{22})\)	None		✓			322.2.i.a	$2$	$0$	\(1\)	\(-3\)	\(5\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\zeta_{22}^{4}q^{2}+(-1-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
322.2.i.b	$322$	$2$	322.i	23.c	$11$	$10$	$1$	$2.571$	\(\Q(\zeta_{22})\)	None		✓			322.2.i.b	$2$	$0$	\(1\)	\(5\)	\(8\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\zeta_{22}^{4}q^{2}+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
322.2.i.c	$322$	$2$	322.i	23.c	$11$	$20$	$2$	$2.571$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			322.2.i.c	$2$	$0$	\(-2\)	\(4\)	\(-5\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{19}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
322.2.i.d	$322$	$2$	322.i	23.c	$11$	$40$	$4$	$2.571$		None		✓			322.2.i.d	$2$	$0$	\(-4\)	\(0\)	\(9\)	\(4\)		$\mathrm{SU}(2)[C_{11}]$
322.2.i.e	$322$	$2$	322.i	23.c	$11$	$40$	$4$	$2.571$		None		✓			322.2.i.e	$2$	$0$	\(4\)	\(2\)	\(-9\)	\(-4\)		$\mathrm{SU}(2)[C_{11}]$

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

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