Space of modular forms of level 535, weight 2, and trivial character

• Label: 535.2.a
• Level: $535$
• Weight: $2$
• Character orbit: 535.a
• Rep. character: $\chi_{535}(1,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $4$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 535 = 5 \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	535.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(535))\).

	Total	New	Old
Modular forms	56	35	21
Cusp forms	53	35	18
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.

\(5\)	\(107\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	$-$	\(15\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(11\)
Minus space		\(-\)	\(24\)

Trace form

\( 35 q + 3 q^{2} + 37 q^{4} + q^{5} - 4 q^{7} + 3 q^{8} + 39 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(535))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	107
535.2.a.a	$535$	$2$	535.a	1.a	$1$	$3$	$3$	$4.272$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
535.2.a.b	$535$	$2$	535.a	1.a	$1$	$8$	$8$	$4.272$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-4\)	\(-2\)	\(-8\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{7}q^{3}+(1-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
535.2.a.c	$535$	$2$	535.a	1.a	$1$	$9$	$9$	$4.272$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(2\)	\(-9\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
535.2.a.d	$535$	$2$	535.a	1.a	$1$	$15$	$15$	$4.272$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(15\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(535))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(535)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(107))\)\(^{\oplus 2}\)