Space of modular forms of level 69, weight 2, and Character 69.e

• Label: 69.2.e
• Level: $69$
• Weight: $2$
• Character orbit: 69.e
• Rep. character: $\chi_{69}(4,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(69, [\chi])\).

	Total	New	Old
Modular forms	100	40	60
Cusp forms	60	40	20
Eisenstein series	40	0	40

Trace form

40 * q - 4 * q^2 - 12 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9 - 8 * q^10 - 24 * q^11 - 8 * q^13 - 12 * q^14 - 8 * q^15 + 16 * q^16 + 10 * q^17 - 4 * q^18 - 10 * q^19 + 52 * q^20 - 4 * q^21 + 4 * q^22 + 20 * q^23 - 12 * q^24 + 16 * q^25 - 12 * q^26 + 24 * q^28 - 10 * q^29 - 28 * q^30 - 10 * q^31 - 24 * q^32 - 8 * q^33 - 26 * q^34 - 12 * q^35 + 10 * q^36 + 4 * q^37 + 58 * q^38 + 36 * q^39 - 58 * q^40 + 4 * q^41 + 78 * q^42 - 12 * q^43 + 50 * q^44 - 4 * q^45 + 20 * q^46 + 48 * q^47 + 56 * q^48 - 52 * q^49 + 46 * q^50 + 12 * q^51 + 6 * q^52 + 8 * q^53 + 18 * q^54 + 2 * q^55 - 6 * q^56 + 32 * q^57 - 6 * q^58 - 12 * q^59 - 26 * q^60 - 12 * q^61 - 120 * q^62 - 8 * q^63 - 20 * q^64 - 64 * q^65 - 40 * q^66 - 42 * q^67 - 92 * q^68 - 20 * q^69 - 56 * q^70 - 64 * q^71 - 12 * q^72 - 34 * q^73 - 74 * q^74 - 24 * q^75 + 30 * q^76 - 8 * q^77 - 16 * q^78 + 36 * q^79 + 10 * q^80 - 4 * q^81 + 8 * q^82 - 16 * q^83 - 52 * q^84 + 114 * q^85 + 48 * q^86 - 32 * q^87 + 8 * q^88 + 56 * q^89 - 8 * q^90 + 72 * q^91 + 30 * q^92 - 40 * q^93 + 54 * q^94 + 78 * q^95 - 24 * q^96 + 36 * q^97 + 116 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(69, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
69.2.e.a	$69$	$2$	69.e	23.c	$11$	$10$	$1$	$0.551$	\(\Q(\zeta_{22})\)	None		✓			69.2.e.a	$2$	$0$	\(-4\)	\(1\)	\(5\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
69.2.e.b	$69$	$2$	69.e	23.c	$11$	$10$	$1$	$0.551$	\(\Q(\zeta_{22})\)	None		✓			69.2.e.b	$2$	$0$	\(4\)	\(1\)	\(-3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots\)
69.2.e.c	$69$	$2$	69.e	23.c	$11$	$20$	$2$	$0.551$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		69.2.e.c	$2$	$0$	\(-4\)	\(-2\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(69, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(69, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)