Space of modular forms of level 11, weight 6, and trivial character

• Label: 11.6.a
• Level: $11$
• Weight: $6$
• Character orbit: 11.a
• Rep. character: $\chi_{11}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(11))\).

	Total	New	Old
Modular forms	6	4	2
Cusp forms	4	4	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.

\(11\)	Dim
\(+\)	\(1\)
\(-\)	\(3\)

Trace form

4 * q - 4 * q^2 + 19 * q^3 + 68 * q^4 + 5 * q^5 - 146 * q^6 + 94 * q^7 - 372 * q^8 - 25 * q^9 - 338 * q^10 + 242 * q^11 + 1232 * q^12 - 662 * q^13 - 1060 * q^14 + 1939 * q^15 + 1736 * q^16 + 1772 * q^17 - 3634 * q^18 + 996 * q^19 - 3176 * q^20 - 1058 * q^21 + 484 * q^22 + 643 * q^23 - 14628 * q^24 - 2821 * q^25 + 16724 * q^26 + 925 * q^27 + 23552 * q^28 - 8850 * q^29 + 1510 * q^30 - 10541 * q^31 - 17528 * q^32 + 5929 * q^33 + 22576 * q^34 - 24418 * q^35 + 5044 * q^36 + 29787 * q^37 - 7704 * q^38 + 10660 * q^39 - 18924 * q^40 + 4466 * q^41 - 47228 * q^42 - 30234 * q^43 + 12100 * q^44 + 18800 * q^45 - 31642 * q^46 - 10064 * q^47 + 64904 * q^48 + 31824 * q^49 + 52126 * q^50 - 33014 * q^51 - 16936 * q^52 + 20724 * q^53 + 3154 * q^54 + 5203 * q^55 - 40392 * q^56 + 25920 * q^57 - 7476 * q^58 - 10199 * q^59 - 18016 * q^60 + 1506 * q^61 + 5798 * q^62 - 12676 * q^63 + 8320 * q^64 + 14144 * q^65 - 32186 * q^66 - 17755 * q^67 - 23576 * q^68 - 20593 * q^69 - 122612 * q^70 + 70305 * q^71 - 98496 * q^72 + 17350 * q^73 + 105042 * q^74 + 19544 * q^75 + 110064 * q^76 + 8954 * q^77 + 56104 * q^78 + 190286 * q^79 + 123544 * q^80 - 141268 * q^81 - 249260 * q^82 - 246642 * q^83 + 346016 * q^84 - 117074 * q^85 + 259164 * q^86 + 61992 * q^87 - 91476 * q^88 - 89409 * q^89 + 102056 * q^90 - 121112 * q^91 - 395872 * q^92 + 80023 * q^93 - 103600 * q^94 - 14904 * q^95 + 344 * q^96 + 76589 * q^97 + 70308 * q^98 + 1331 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\) 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
11.6.a.a	$11$	$6$	11.a	1.a	$1$	$1$	$1$	$1.764$	\(\Q\)	None	✓	✓	✓	✓	11.6.a.a	$1$	$1$	\(-4\)	\(-15\)	\(-19\)	\(10\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}+60q^{6}+\cdots\)
11.6.a.b	$11$	$6$	11.a	1.a	$1$	$3$	$3$	$1.764$	3.3.54492.1	None	✓	✓	✓	✓	11.6.a.b	$1$	$0$	\(0\)	\(34\)	\(24\)	\(84\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)