Space of modular forms of level 77, weight 2, and Character 77.f

• Label: 77.2.f
• Level: $77$
• Weight: $2$
• Character orbit: 77.f
• Rep. character: $\chi_{77}(15,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(77, [\chi])\).

	Total	New	Old
Modular forms	40	24	16
Cusp forms	24	24	0
Eisenstein series	16	0	16

Trace form

24 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 2 * q^5 + 6 * q^6 - 2 * q^7 - 2 * q^8 - 14 * q^9 - 16 * q^10 + 2 * q^11 + 4 * q^12 - 2 * q^13 + 3 * q^14 - 12 * q^15 + 14 * q^16 - 16 * q^17 + 15 * q^18 + 10 * q^19 + 22 * q^20 + 12 * q^21 - 34 * q^22 + 16 * q^23 - 14 * q^24 + 12 * q^25 - 6 * q^26 - 12 * q^27 + 11 * q^28 - 6 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^32 - 16 * q^33 - 48 * q^34 - 8 * q^35 + 50 * q^36 + 10 * q^37 + 30 * q^38 + 6 * q^39 - 26 * q^40 - 32 * q^41 + 8 * q^43 - 9 * q^44 + 88 * q^45 - 13 * q^46 - 16 * q^47 - 32 * q^48 - 6 * q^49 + 18 * q^50 - 26 * q^51 + 54 * q^52 + 6 * q^53 + 64 * q^54 + 14 * q^55 - 18 * q^56 - 14 * q^57 - 19 * q^58 + 42 * q^59 - 68 * q^60 + 74 * q^62 - 10 * q^63 + 8 * q^64 + 16 * q^65 + 26 * q^66 - 68 * q^67 + 6 * q^68 + 18 * q^69 - 20 * q^70 - 28 * q^71 + 3 * q^72 - 32 * q^73 - 38 * q^74 + 14 * q^75 - 8 * q^77 - 76 * q^78 + 6 * q^79 - 120 * q^80 - 42 * q^81 + 50 * q^82 + 28 * q^83 + 12 * q^84 - 4 * q^85 - 69 * q^86 - 60 * q^87 + 48 * q^88 + 40 * q^89 - 12 * q^90 + 18 * q^91 - 89 * q^92 + 40 * q^93 - 54 * q^94 + 56 * q^95 - 32 * q^96 + 50 * q^97 + 6 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(77, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
77.2.f.a	$77$	$2$	77.f	11.c	$5$	$8$	$2$	$0.615$	8.0.159390625.1	None		✓			77.2.f.a	$2$	$0$	\(-1\)	\(-4\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
77.2.f.b	$77$	$2$	77.f	11.c	$5$	$16$	$4$	$0.615$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		77.2.f.b	$2$	$0$	\(-3\)	\(-2\)	\(-5\)	\(-4\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{5}-\beta _{6})q^{2}+(\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)