Space of modular forms of level 67, weight 2, and Character 67.e

• Label: 67.2.e
• Level: $67$
• Weight: $2$
• Character orbit: 67.e
• Rep. character: $\chi_{67}(9,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $11$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(11\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(67, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	40	40	0
Eisenstein series	20	20	0

Trace form

40 * q - 6 * q^2 - 3 * q^3 - 8 * q^4 - 5 * q^5 + q^6 - q^7 - 23 * q^8 + 3 * q^9 - 32 * q^10 + 3 * q^11 - 12 * q^12 + 9 * q^13 + 11 * q^14 - 11 * q^15 + 14 * q^16 - 29 * q^17 + 16 * q^18 - 10 * q^19 + 33 * q^20 - 41 * q^21 - 16 * q^22 - 11 * q^23 - 11 * q^24 + 5 * q^25 + 21 * q^26 + 27 * q^27 + 16 * q^28 - 2 * q^29 + 16 * q^30 - 11 * q^31 + 11 * q^32 + 12 * q^33 + 41 * q^34 + 31 * q^35 + 45 * q^36 + 4 * q^37 - 56 * q^38 - 37 * q^39 - 4 * q^40 - 4 * q^41 + 77 * q^42 - 3 * q^43 + 67 * q^44 - 31 * q^45 - 4 * q^46 + 27 * q^47 + q^48 + 51 * q^49 - 56 * q^50 + 55 * q^51 - 81 * q^52 + 40 * q^53 - 61 * q^54 + 10 * q^55 - 17 * q^56 - 15 * q^57 - q^58 - 81 * q^59 + 65 * q^60 - 63 * q^61 + 65 * q^62 - 44 * q^63 - 27 * q^64 + 11 * q^65 - 138 * q^66 + 33 * q^67 - 196 * q^68 + 71 * q^69 - 41 * q^70 + 5 * q^71 - 58 * q^72 - 70 * q^73 + 51 * q^74 - 70 * q^75 + 23 * q^76 - 85 * q^77 + 129 * q^78 - 48 * q^79 + 67 * q^80 + 44 * q^81 - 40 * q^82 + 49 * q^83 - 15 * q^84 + 51 * q^85 - 75 * q^86 - 14 * q^87 + 57 * q^88 + 55 * q^89 + 21 * q^90 - 5 * q^91 + 65 * q^92 - 75 * q^93 + 65 * q^94 + 92 * q^95 - 6 * q^96 + 30 * q^97 + 140 * q^98 + 112 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(67, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
67.2.e.a	$67$	$2$	67.e	67.e	$11$	$10$	$1$	$0.535$	\(\Q(\zeta_{22})\)	None		✓			67.2.e.a	$2$	$0$	\(-6\)	\(-2\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1-\zeta_{22}^{2}-\zeta_{22}^{4}+\zeta_{22}^{7}-\zeta_{22}^{8}+\cdots)q^{2}+\cdots\)
67.2.e.b	$67$	$2$	67.e	67.e	$11$	$10$	$1$	$0.535$	\(\Q(\zeta_{22})\)	None		✓			67.2.e.b	$2$	$0$	\(4\)	\(3\)	\(-9\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\zeta_{22}+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}+\cdots)q^{2}+\cdots\)
67.2.e.c	$67$	$2$	67.e	67.e	$11$	$20$	$2$	$0.535$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		67.2.e.c	$2$	$0$	\(-4\)	\(-4\)	\(1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\beta _{9}-\beta _{14})q^{2}-\beta _{19}q^{3}+(-1+\cdots)q^{4}+\cdots\)