Space of modular forms of level 121, weight 4, and trivial character

• Label: 121.4.a
• Level: $121$
• Weight: $4$
• Character orbit: 121.a
• Rep. character: $\chi_{121}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $8$
• Sturm bound: $44$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(44\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(121))\).

	Total	New	Old
Modular forms	39	32	7
Cusp forms	27	23	4
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
\(+\)	\(13\)
\(-\)	\(10\)

Trace form

\( 23 q - 2 q^{2} + 88 q^{4} + 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} + 107 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(121))\) 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
121.4.a.a	$121$	$4$	121.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(8\)	\(18\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+8q^{3}-8q^{4}+18q^{5}+37q^{9}-2^{6}q^{12}+\cdots\)
121.4.a.b	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(-8\)	\(-10\)	\(-8\)		$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-4+\beta )q^{3}+(5-2\beta )q^{4}+\cdots\)
121.4.a.c	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(2\)	\(-20\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots\)
121.4.a.d	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	\(\Q(\sqrt{26}) \)	None	✓	$2$	$0$	\(0\)	\(-10\)	\(10\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-5q^{3}+18q^{4}+5q^{5}-5\beta q^{6}+\cdots\)
121.4.a.e	$121$	$4$	121.a	1.a	$1$	$2$	$2$	$7.139$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(2\)	\(-8\)	\(-10\)	\(8\)		$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(5+2\beta )q^{4}+\cdots\)
121.4.a.f	$121$	$4$	121.a	1.a	$1$	$4$	$4$	$7.139$	\(\Q(\sqrt{5}, \sqrt{37})\)	None	✓	$1$	$1$	\(-4\)	\(6\)	\(-11\)	\(-25\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+\cdots\)
121.4.a.g	$121$	$4$	121.a	1.a	$1$	$4$	$4$	$7.139$	\(\Q(\sqrt{5}, \sqrt{37})\)	None	✓	$1$	$0$	\(4\)	\(6\)	\(-11\)	\(25\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(2+\beta _{2})q^{3}+(3+\cdots)q^{4}+\cdots\)
121.4.a.h	$121$	$4$	121.a	1.a	$1$	$6$	$6$	$7.139$	6.6.\(\cdots\).1	None	✓	$2$	$0$	\(0\)	\(8\)	\(14\)	\(0\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(3+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(121)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)