Space of modular forms of level 121, weight 14, and trivial character

• Label: 121.14.a
• Level: $121$
• Weight: $14$
• Character orbit: 121.a
• Rep. character: $\chi_{121}(1,\cdot)$
• Character field: $\Q$
• Dimension: $113$
• Newform subspaces: $9$
• Sturm bound: $154$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(154\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(121))\).

	Total	New	Old
Modular forms	149	122	27
Cusp forms	137	113	24
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
\(+\)	\(55\)
\(-\)	\(58\)

Trace form

\( 113 q + 64 q^{2} - 1458 q^{3} + 446828 q^{4} - 73114 q^{5} + 269570 q^{6} + 403306 q^{7} + 835572 q^{8} + 55459247 q^{9} + O(q^{10}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(121))\) 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
121.14.a.a	$121$	$14$	121.a	1.a	$1$	$1$	$1$	$129.749$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓			121.14.a.a	$2$	$1$	\(0\)	\(1559\)	\(9357\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+1559q^{3}-2^{13}q^{4}+9357q^{5}+836158q^{9}+\cdots\)
121.14.a.b	$121$	$14$	121.a	1.a	$1$	$5$	$5$	$129.749$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				11.14.a.a	$1$	$0$	\(64\)	\(480\)	\(-454\)	\(313920\)		$-$	$-$	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(13+\beta _{1})q^{2}+(96-2\beta _{1}-\beta _{3})q^{3}+\cdots\)
121.14.a.c	$121$	$14$	121.a	1.a	$1$	$7$	$7$	$129.749$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				11.14.a.b	$1$	$0$	\(0\)	\(379\)	\(52689\)	\(89386\)		$-$	$-$	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(54+3\beta _{1}-\beta _{2})q^{3}+(6727+\cdots)q^{4}+\cdots\)
121.14.a.d	$121$	$14$	121.a	1.a	$1$	$10$	$10$	$129.749$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			121.14.a.d	$2$	$1$	\(0\)	\(-3616\)	\(-121028\)	\(0\)		$+$	$+$	$2^{19}\cdot 3^{3}\cdot 11^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-362-\beta _{2})q^{3}+(7409+\cdots)q^{4}+\cdots\)
121.14.a.e	$121$	$14$	121.a	1.a	$1$	$11$	$11$	$129.749$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			121.14.a.e	$1$	$0$	\(-64\)	\(130\)	\(-10561\)	\(-132498\)		$-$	$-$	$2^{19}\cdot 3^{5}\cdot 11^{4}$	$\mathrm{SU}(2)$	\(q+(-6+\beta _{1})q^{2}+(12-2\beta _{1}+\beta _{3})q^{3}+\cdots\)
121.14.a.f	$121$	$14$	121.a	1.a	$1$	$11$	$11$	$129.749$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓			121.14.a.e	$1$	$0$	\(64\)	\(130\)	\(-10561\)	\(132498\)		$-$	$-$	$2^{19}\cdot 3^{5}\cdot 11^{4}$	$\mathrm{SU}(2)$	\(q+(6-\beta _{1})q^{2}+(12-2\beta _{1}+\beta _{3})q^{3}+\cdots\)
121.14.a.g	$121$	$14$	121.a	1.a	$1$	$20$	$20$	$129.749$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓			121.14.a.g	$2$	$1$	\(0\)	\(-2656\)	\(-44716\)	\(0\)		$+$	$+$	$2^{28}\cdot 3^{2}\cdot 11^{16}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-133-\beta _{2})q^{3}+(2440+\cdots)q^{4}+\cdots\)
121.14.a.h	$121$	$14$	121.a	1.a	$1$	$24$	$24$	$129.749$		None	✓		✓		11.14.c.a	$1$	$1$	\(-128\)	\(1068\)	\(26080\)	\(-386592\)		$+$	$+$		$\mathrm{SU}(2)$
121.14.a.i	$121$	$14$	121.a	1.a	$1$	$24$	$24$	$129.749$		None	✓		✓		11.14.c.a	$1$	$0$	\(128\)	\(1068\)	\(26080\)	\(386592\)		$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(121))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(121)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)