Space of modular forms of level 121, weight 6, and trivial character

• Label: 121.6.a
• Level: $121$
• Weight: $6$
• Character orbit: 121.a
• Rep. character: $\chi_{121}(1,\cdot)$
• Character field: $\Q$
• Dimension: $41$
• Newform subspaces: $9$
• Sturm bound: $66$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(66\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(121))\).

	Total	New	Old
Modular forms	61	50	11
Cusp forms	49	41	8
Eisenstein series	12	9	3

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
\(+\)	\(19\)
\(-\)	\(22\)

Trace form

\( 41 q + 4 q^{2} - 18 q^{3} + 572 q^{4} - 34 q^{5} + 146 q^{6} - 94 q^{7} + 372 q^{8} + 2891 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(121))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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
121.6.a.a	$121$	$6$	121.a	1.a	$1$	$1$	$1$	$19.406$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$1$	\(0\)	\(-31\)	\(57\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-31q^{3}-2^{5}q^{4}+57q^{5}+718q^{9}+\cdots\)
121.6.a.b	$121$	$6$	121.a	1.a	$1$	$1$	$1$	$19.406$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(-15\)	\(-19\)	\(-10\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}-60q^{6}+\cdots\)
121.6.a.c	$121$	$6$	121.a	1.a	$1$	$2$	$2$	$19.406$	\(\Q(\sqrt{38}) \)	None	✓	$2$	$1$	\(0\)	\(14\)	\(-38\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+7q^{3}+6q^{4}-19q^{5}+7\beta q^{6}+\cdots\)
121.6.a.d	$121$	$6$	121.a	1.a	$1$	$3$	$3$	$19.406$	3.3.54492.1	None	✓	$1$	$0$	\(0\)	\(34\)	\(24\)	\(-84\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)
121.6.a.e	$121$	$6$	121.a	1.a	$1$	$5$	$5$	$19.406$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(-4\)	\(10\)	\(29\)	\(102\)		$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{1}+\beta _{2})q^{3}+\cdots\)
121.6.a.f	$121$	$6$	121.a	1.a	$1$	$5$	$5$	$19.406$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(10\)	\(29\)	\(-102\)		$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2+\beta _{1}+\beta _{2})q^{3}+(21+\cdots)q^{4}+\cdots\)
121.6.a.g	$121$	$6$	121.a	1.a	$1$	$8$	$8$	$19.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(-12\)	\(70\)	\(-292\)		$+$	$+$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-2-\beta _{6})q^{3}+(11+\cdots)q^{4}+\cdots\)
121.6.a.h	$121$	$6$	121.a	1.a	$1$	$8$	$8$	$19.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(-16\)	\(-256\)	\(0\)		$+$	$+$	$2^{4}\cdot 11$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-2+\beta _{6})q^{3}+(19-\beta _{2}+\cdots)q^{4}+\cdots\)
121.6.a.i	$121$	$6$	121.a	1.a	$1$	$8$	$8$	$19.406$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(-12\)	\(70\)	\(292\)		$-$	$-$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-2-\beta _{6})q^{3}+(11-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(121)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)