Space of modular forms of level 4334, weight 2, and trivial character

• Label: 4334.2.a
• Level: $4334$
• Weight: $2$
• Character orbit: 4334.a
• Rep. character: $\chi_{4334}(1,\cdot)$
• Character field: $\Q$
• Dimension: $165$
• Newform subspaces: $8$
• Sturm bound: $1188$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1188\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4334))\).

	Total	New	Old
Modular forms	598	165	433
Cusp forms	591	165	426
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(11\)	\(197\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(17\)
\(+\)	\(+\)	\(-\)	$-$	\(24\)
\(+\)	\(-\)	\(+\)	$-$	\(27\)
\(+\)	\(-\)	\(-\)	$+$	\(15\)
\(-\)	\(+\)	\(+\)	$-$	\(24\)
\(-\)	\(+\)	\(-\)	$+$	\(17\)
\(-\)	\(-\)	\(+\)	$+$	\(15\)
\(-\)	\(-\)	\(-\)	$-$	\(26\)
Plus space			\(+\)	\(64\)
Minus space			\(-\)	\(101\)

Trace form

\( 165 q - q^{2} + 4 q^{3} + 165 q^{4} + 2 q^{5} + 4 q^{6} + 8 q^{7} - q^{8} + 173 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	11	197
4334.2.a.a	$4334$	$2$	4334.a	1.a	$1$	$15$	$15$	$34.607$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-15\)	\(-1\)	\(-7\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
4334.2.a.b	$4334$	$2$	4334.a	1.a	$1$	$15$	$15$	$34.607$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(15\)	\(-9\)	\(-11\)	\(-11\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
4334.2.a.c	$4334$	$2$	4334.a	1.a	$1$	$17$	$17$	$34.607$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$1$	\(-17\)	\(5\)	\(6\)	\(-9\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
4334.2.a.d	$4334$	$2$	4334.a	1.a	$1$	$17$	$17$	$34.607$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$1$	\(17\)	\(-7\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$5$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots\)
4334.2.a.e	$4334$	$2$	4334.a	1.a	$1$	$24$	$24$	$34.607$		None	✓	$1$	$0$	\(-24\)	\(-4\)	\(-4\)	\(7\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4334.2.a.f	$4334$	$2$	4334.a	1.a	$1$	$24$	$24$	$34.607$		None	✓	$1$	$0$	\(24\)	\(8\)	\(0\)	\(11\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
4334.2.a.g	$4334$	$2$	4334.a	1.a	$1$	$26$	$26$	$34.607$		None	✓	$1$	$0$	\(26\)	\(12\)	\(13\)	\(13\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
4334.2.a.h	$4334$	$2$	4334.a	1.a	$1$	$27$	$27$	$34.607$		None	✓	$1$	$0$	\(-27\)	\(0\)	\(9\)	\(1\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4334)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(197))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(394))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2167))\)\(^{\oplus 2}\)