Space of modular forms of level 11, weight 6, and Character 11.c

• Label: 11.6.c
• Level: $11$
• Weight: $6$
• Character orbit: 11.c
• Rep. character: $\chi_{11}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(11, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	16	16	0
Eisenstein series	8	8	0

Trace form

16 * q - q^2 - 24 * q^3 - 73 * q^4 - 10 * q^5 + 121 * q^6 + 196 * q^7 + 527 * q^8 - 530 * q^9 - 672 * q^10 - 692 * q^11 - 1562 * q^12 + 1162 * q^13 + 560 * q^14 + 1796 * q^15 + 6399 * q^16 - 22 * q^17 + 834 * q^18 - 3236 * q^19 - 5514 * q^20 - 7772 * q^21 - 13059 * q^22 - 10848 * q^23 + 13233 * q^24 + 15686 * q^25 + 16216 * q^26 + 22500 * q^27 + 8838 * q^28 + 13070 * q^29 - 22830 * q^30 - 14764 * q^31 - 58812 * q^32 - 48544 * q^33 - 26966 * q^34 + 43368 * q^35 + 63696 * q^36 + 4638 * q^37 + 68144 * q^38 + 20300 * q^39 + 52284 * q^40 - 14806 * q^41 - 69922 * q^42 - 24376 * q^43 - 104960 * q^44 - 97480 * q^45 + 50452 * q^46 + 40364 * q^47 + 30236 * q^48 + 32246 * q^49 + 10839 * q^50 + 75564 * q^51 - 80654 * q^52 - 11654 * q^53 + 43796 * q^54 + 7052 * q^55 + 70632 * q^56 - 40020 * q^57 + 10276 * q^58 + 70804 * q^59 + 46116 * q^60 - 31446 * q^61 - 153388 * q^62 - 7064 * q^63 + 17695 * q^64 - 41284 * q^65 + 48006 * q^66 - 64200 * q^67 - 94114 * q^68 - 62412 * q^69 - 103768 * q^70 - 184380 * q^71 - 14729 * q^72 - 1750 * q^73 + 306048 * q^74 + 246596 * q^75 + 174806 * q^76 + 384646 * q^77 + 360916 * q^78 + 24324 * q^79 - 386444 * q^80 - 259412 * q^81 - 316255 * q^82 - 46028 * q^83 - 271956 * q^84 + 63914 * q^85 + 22931 * q^86 - 47592 * q^87 + 211871 * q^88 + 148364 * q^89 - 347186 * q^90 - 258448 * q^91 - 58658 * q^92 - 387478 * q^93 - 55370 * q^94 - 4716 * q^95 + 328396 * q^96 + 484296 * q^97 + 743692 * q^98 + 724964 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(11, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.6.c.a	$11$	$6$	11.c	11.c	$5$	$16$	$4$	$1.764$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	11.6.c.a	$2$	$0$	\(-1\)	\(-24\)	\(-10\)	\(196\)	$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{2}+\cdots\)