Space of modular forms of level 121, weight 10, and trivial character

• Label: 121.10.a
• Level: $121$
• Weight: $10$
• Character orbit: 121.a
• Rep. character: $\chi_{121}(1,\cdot)$
• Character field: $\Q$
• Dimension: $77$
• Newform subspaces: $9$
• Sturm bound: $110$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(110\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(121))\).

	Total	New	Old
Modular forms	105	86	19
Cusp forms	93	77	16
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
\(+\)	\(37\)
\(-\)	\(40\)

Trace form

\( 77 q - 16 q^{2} + 18860 q^{4} + 1026 q^{5} + 578 q^{6} - 1140 q^{7} - 20652 q^{8} + 392669 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(121))\) 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
121.10.a.a	$121$	$10$	121.a	1.a	$1$	$1$	$1$	$62.319$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓			121.10.a.a	$2$	$1$	\(0\)	\(-136\)	\(-918\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-136q^{3}-2^{9}q^{4}-918q^{5}-1187q^{9}+\cdots\)
121.10.a.b	$121$	$10$	121.a	1.a	$1$	$3$	$3$	$62.319$	3.3.2659452.1	None	✓				11.10.a.a	$1$	$0$	\(0\)	\(-186\)	\(-1824\)	\(7260\)		$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-62+4\beta _{1}-\beta _{2})q^{3}+(304+\cdots)q^{4}+\cdots\)
121.10.a.c	$121$	$10$	121.a	1.a	$1$	$5$	$5$	$62.319$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				11.10.a.b	$1$	$0$	\(-16\)	\(112\)	\(1594\)	\(-8400\)		$-$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots\)
121.10.a.d	$121$	$10$	121.a	1.a	$1$	$6$	$6$	$62.319$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			121.10.a.d	$2$	$1$	\(0\)	\(62\)	\(342\)	\(0\)		$+$	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(10+\beta _{4})q^{3}+(456+\beta _{3}+\cdots)q^{4}+\cdots\)
121.10.a.e	$121$	$10$	121.a	1.a	$1$	$8$	$8$	$62.319$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			121.10.a.e	$1$	$0$	\(-16\)	\(88\)	\(3184\)	\(-456\)		$-$	$-$	$2^{12}\cdot 3^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(11+\beta _{3})q^{3}+(331+\cdots)q^{4}+\cdots\)
121.10.a.f	$121$	$10$	121.a	1.a	$1$	$8$	$8$	$62.319$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			121.10.a.e	$1$	$0$	\(16\)	\(88\)	\(3184\)	\(456\)		$-$	$-$	$2^{12}\cdot 3^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+(11+\beta _{3})q^{3}+(331-2\beta _{1}+\cdots)q^{4}+\cdots\)
121.10.a.g	$121$	$10$	121.a	1.a	$1$	$14$	$14$	$62.319$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓			121.10.a.g	$2$	$1$	\(0\)	\(-472\)	\(-786\)	\(0\)		$+$	$+$	$2^{12}\cdot 3\cdot 11^{8}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-34+\beta _{3})q^{3}+(171-\beta _{3}+\cdots)q^{4}+\cdots\)
121.10.a.h	$121$	$10$	121.a	1.a	$1$	$16$	$16$	$62.319$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		11.10.c.a	$1$	$1$	\(-48\)	\(222\)	\(-1875\)	\(-12575\)		$+$	$+$	$2^{14}\cdot 3^{4}\cdot 11^{9}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{2}+(14-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{3}+\cdots\)
121.10.a.i	$121$	$10$	121.a	1.a	$1$	$16$	$16$	$62.319$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		11.10.c.a	$1$	$0$	\(48\)	\(222\)	\(-1875\)	\(12575\)		$-$	$-$	$2^{14}\cdot 3^{4}\cdot 11^{9}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(14-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(121)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)