Space of modular forms of level 11, weight 8, and trivial character

• Label: 11.8.a
• Level: $11$
• Weight: $8$
• Character orbit: 11.a
• Rep. character: $\chi_{11}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(11))\).

	Total	New	Old
Modular forms	8	6	2
Cusp forms	6	6	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(11\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(5\)	\(4\)	\(1\)		\(4\)	\(4\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

6 * q - 8 * q^2 - 41 * q^3 + 500 * q^4 + 67 * q^5 + 862 * q^6 - 1058 * q^7 + 60 * q^8 + 1787 * q^9 + 5750 * q^10 - 2662 * q^11 - 28288 * q^12 + 4594 * q^13 - 15236 * q^14 - 6149 * q^15 + 46376 * q^16 + 45832 * q^17 - 66886 * q^18 + 32564 * q^19 + 21128 * q^20 + 46906 * q^21 - 10648 * q^22 - 70501 * q^23 + 245964 * q^24 + 24731 * q^25 - 250916 * q^26 - 135695 * q^27 - 490704 * q^28 + 413118 * q^29 - 256826 * q^30 + 132691 * q^31 + 11192 * q^32 + 38599 * q^33 + 488 * q^34 + 639478 * q^35 + 815092 * q^36 - 749803 * q^37 - 801480 * q^38 - 1384652 * q^39 + 1781268 * q^40 + 6226 * q^41 + 1680964 * q^42 + 980414 * q^43 - 942348 * q^44 - 1851892 * q^45 + 4279846 * q^46 - 66568 * q^47 - 7055896 * q^48 + 53706 * q^49 - 3252718 * q^50 + 617266 * q^51 + 1514952 * q^52 + 2715144 * q^53 + 6445090 * q^54 - 1340317 * q^55 - 6062760 * q^56 + 3819120 * q^57 - 1046220 * q^58 - 7119907 * q^59 + 752912 * q^60 - 5708566 * q^61 + 6940534 * q^62 + 859244 * q^63 + 10607904 * q^64 + 5688520 * q^65 - 3000074 * q^66 - 3542943 * q^67 + 18917816 * q^68 + 4250597 * q^69 - 18308116 * q^70 - 4568007 * q^71 - 26184720 * q^72 + 12352174 * q^73 - 13520406 * q^74 + 9979160 * q^75 + 6867104 * q^76 - 1860738 * q^77 + 1427848 * q^78 + 4367742 * q^79 + 1481336 * q^80 - 10193266 * q^81 - 1752916 * q^82 - 6503706 * q^83 + 14049200 * q^84 + 3504482 * q^85 - 5562708 * q^86 - 9064920 * q^87 + 1197900 * q^88 + 4783221 * q^89 + 13795712 * q^90 + 3752424 * q^91 - 7320368 * q^92 - 1131947 * q^93 - 15632 * q^94 - 4528968 * q^95 + 19662920 * q^96 + 11357247 * q^97 + 24721536 * q^98 - 2474329 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(11))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11
11.8.a.a	$11$	$8$	11.a	1.a	$1$	$2$	$2$	$3.436$	\(\Q(\sqrt{15}) \)	None	✓	✓	✓	✓	11.8.a.a	$1$	$1$	\(-8\)	\(-6\)	\(-470\)	\(-1228\)		$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-4+\beta )q^{2}+(-3-6\beta )q^{3}+(-52+\cdots)q^{4}+\cdots\)
11.8.a.b	$11$	$8$	11.a	1.a	$1$	$4$	$4$	$3.436$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	11.8.a.b	$1$	$0$	\(0\)	\(-35\)	\(537\)	\(170\)		$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-9-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)