Space of modular forms of level 1343, weight 2, and trivial character

• Label: 1343.2.a
• Level: $1343$
• Weight: $2$
• Character orbit: 1343.a
• Rep. character: $\chi_{1343}(1,\cdot)$
• Character field: $\Q$
• Dimension: $105$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1343 = 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1343.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1343))\).

	Total	New	Old
Modular forms	122	105	17
Cusp forms	119	105	14
Eisenstein series	3	0	3

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

\(17\)	\(79\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(20\)
\(+\)	\(-\)	$-$	\(32\)
\(-\)	\(+\)	$-$	\(37\)
\(-\)	\(-\)	$+$	\(16\)
Plus space		\(+\)	\(36\)
Minus space		\(-\)	\(69\)

Trace form

\( 105 q + 3 q^{2} + 111 q^{4} - 2 q^{5} - 8 q^{6} + 8 q^{7} - 9 q^{8} + 105 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1343))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		17	79
1343.2.a.a	$1343$	$2$	1343.a	1.a	$1$	$1$	$1$	$10.724$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1343.2.a.b	$1343$	$2$	1343.a	1.a	$1$	$15$	$15$	$10.724$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-5\)	\(-4\)	\(-14\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
1343.2.a.c	$1343$	$2$	1343.a	1.a	$1$	$20$	$20$	$10.724$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-4\)	\(-7\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}-\beta _{15}q^{5}+\cdots\)
1343.2.a.d	$1343$	$2$	1343.a	1.a	$1$	$32$	$32$	$10.724$		None	✓	$1$	$0$	\(2\)	\(6\)	\(5\)	\(21\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1343.2.a.e	$1343$	$2$	1343.a	1.a	$1$	$37$	$37$	$10.724$		None	✓	$1$	$0$	\(6\)	\(2\)	\(3\)	\(11\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1343))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1343)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(79))\)\(^{\oplus 2}\)