Space of modular forms of level 65, weight 6, and Character 65.o

• Label: 65.6.o
• Level: $65$
• Weight: $6$
• Character orbit: 65.o
• Rep. character: $\chi_{65}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $132$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(65, [\chi])\).

	Total	New	Old
Modular forms	148	148	0
Cusp forms	132	132	0
Eisenstein series	16	16	0

Trace form

132 * q + 6 * q^2 - 2 * q^3 - 992 * q^4 + 94 * q^5 - 8 * q^6 - 6 * q^7 - 648 * q^8 - 660 * q^9 - 70 * q^10 + 352 * q^11 - 1456 * q^12 + 2222 * q^13 + 1852 * q^15 - 13828 * q^16 + 2650 * q^17 + 3300 * q^19 + 9614 * q^20 - 1348 * q^21 - 3084 * q^22 - 7122 * q^23 - 9896 * q^24 + 542 * q^25 - 888 * q^26 + 9124 * q^27 + 186 * q^28 + 6794 * q^30 - 23968 * q^31 - 376 * q^32 - 17458 * q^33 + 7128 * q^34 - 33860 * q^35 + 42228 * q^36 + 60702 * q^37 + 128 * q^38 + 19180 * q^39 - 27616 * q^40 + 45882 * q^41 - 15536 * q^42 - 12342 * q^43 - 89432 * q^44 - 52908 * q^45 - 53848 * q^46 + 146168 * q^48 + 138022 * q^49 + 36004 * q^50 - 166534 * q^52 - 14250 * q^53 - 30648 * q^54 + 62106 * q^55 + 138996 * q^56 + 232068 * q^57 - 71310 * q^58 + 82080 * q^59 - 199892 * q^60 + 14136 * q^61 - 137440 * q^62 - 120512 * q^63 + 311552 * q^64 + 240508 * q^65 - 169296 * q^66 - 72058 * q^67 - 320192 * q^68 + 25680 * q^69 - 185768 * q^70 + 30352 * q^71 + 183354 * q^72 + 383792 * q^73 - 240840 * q^74 + 154126 * q^75 - 61272 * q^76 - 55652 * q^77 + 345952 * q^78 - 326674 * q^80 + 65330 * q^81 - 583278 * q^82 + 524288 * q^84 - 87686 * q^85 + 401732 * q^86 - 427858 * q^87 - 1091870 * q^88 - 4170 * q^89 + 116384 * q^90 - 479928 * q^91 + 746232 * q^92 + 100848 * q^93 + 52704 * q^94 + 167134 * q^95 - 555088 * q^96 + 567178 * q^97 - 1033706 * q^98 - 388588 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(65, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
65.6.o.a	$65$	$6$	65.o	65.o	$12$	$132$	$33$	$10.425$		None		✓	✓	✓	65.6.o.a	$2$	$0$	\(6\)	\(-2\)	\(94\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$