Space of modular forms of level 1511, weight 2, and trivial character

• Label: 1511.2.a
• Level: $1511$
• Weight: $2$
• Character orbit: 1511.a
• Rep. character: $\chi_{1511}(1,\cdot)$
• Character field: $\Q$
• Dimension: $126$
• Newform subspaces: $2$
• Sturm bound: $252$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(252\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1511))\).

	Total	New	Old
Modular forms	127	127	0
Cusp forms	126	126	0
Eisenstein series	1	1	0

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

\(1511\)	Dim
\(+\)	\(39\)
\(-\)	\(87\)

Trace form

\( 126 q + q^{2} + 129 q^{4} + 2 q^{5} + 6 q^{7} + 3 q^{8} + 132 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1511))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		1511
1511.2.a.a	$1511$	$2$	1511.a	1.a	$1$	$39$	$39$	$12.065$		None	✓	$1$	$1$	\(-5\)	\(-4\)	\(-8\)	\(-15\)		$+$	$+$		$\mathrm{SU}(2)$
1511.2.a.b	$1511$	$2$	1511.a	1.a	$1$	$87$	$87$	$12.065$		None	✓	$1$	$0$	\(6\)	\(4\)	\(10\)	\(21\)		$-$	$-$		$\mathrm{SU}(2)$