Space of modular forms of level 8046, weight 2, and trivial character

• Label: 8046.2.a
• Level: $8046$
• Weight: $2$
• Character orbit: 8046.a
• Rep. character: $\chi_{8046}(1,\cdot)$
• Character field: $\Q$
• Dimension: $196$
• Newform subspaces: $20$
• Sturm bound: $2700$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8046.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(2700\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8046))\).

	Total	New	Old
Modular forms	1362	196	1166
Cusp forms	1339	196	1143
Eisenstein series	23	0	23

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

\(2\)	\(3\)	\(149\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(+\)	\(-\)	$-$	\(28\)
\(+\)	\(-\)	\(+\)	$-$	\(28\)
\(+\)	\(-\)	\(-\)	$+$	\(21\)
\(-\)	\(+\)	\(+\)	$-$	\(28\)
\(-\)	\(+\)	\(-\)	$+$	\(21\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(28\)
Plus space			\(+\)	\(84\)
Minus space			\(-\)	\(112\)

Trace form

\( 196 q + 196 q^{4} + 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8046))\) 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	3	149
8046.2.a.a	$8046$	$2$	8046.a	1.a	$1$	$1$	$1$	$64.248$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
8046.2.a.b	$8046$	$2$	8046.a	1.a	$1$	$1$	$1$	$64.248$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
8046.2.a.c	$8046$	$2$	8046.a	1.a	$1$	$2$	$2$	$64.248$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2\beta q^{5}+(1-2\beta )q^{7}-q^{8}+\cdots\)
8046.2.a.d	$8046$	$2$	8046.a	1.a	$1$	$2$	$2$	$64.248$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2\beta q^{5}+(1+2\beta )q^{7}+q^{8}+\cdots\)
8046.2.a.e	$8046$	$2$	8046.a	1.a	$1$	$8$	$8$	$64.248$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(0\)	\(0\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
8046.2.a.f	$8046$	$2$	8046.a	1.a	$1$	$8$	$8$	$64.248$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(8\)	\(0\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
8046.2.a.g	$8046$	$2$	8046.a	1.a	$1$	$9$	$9$	$64.248$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(\beta _{1}-\beta _{5}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8046.2.a.h	$8046$	$2$	8046.a	1.a	$1$	$9$	$9$	$64.248$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(9\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{5}+\cdots\)
8046.2.a.i	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-12\)	\(0\)	\(-5\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1-\beta _{5})q^{7}-q^{8}+\cdots\)
8046.2.a.j	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-12\)	\(0\)	\(-3\)	\(6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}-q^{8}+\cdots\)
8046.2.a.k	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-12\)	\(0\)	\(3\)	\(-6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{9})q^{7}+\cdots\)
8046.2.a.l	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-12\)	\(0\)	\(5\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
8046.2.a.m	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(12\)	\(0\)	\(-5\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
8046.2.a.n	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(12\)	\(0\)	\(-3\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{9})q^{7}+\cdots\)
8046.2.a.o	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(0\)	\(3\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{6})q^{7}+q^{8}+\cdots\)
8046.2.a.p	$8046$	$2$	8046.a	1.a	$1$	$12$	$12$	$64.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(0\)	\(5\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{5})q^{7}+q^{8}+\cdots\)
8046.2.a.q	$8046$	$2$	8046.a	1.a	$1$	$14$	$14$	$64.248$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(-14\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{11}q^{7}-q^{8}+\cdots\)
8046.2.a.r	$8046$	$2$	8046.a	1.a	$1$	$14$	$14$	$64.248$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(14\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots\)
8046.2.a.s	$8046$	$2$	8046.a	1.a	$1$	$16$	$16$	$64.248$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(-16\)	\(0\)	\(-4\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{7}q^{7}-q^{8}+\cdots\)
8046.2.a.t	$8046$	$2$	8046.a	1.a	$1$	$16$	$16$	$64.248$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(16\)	\(0\)	\(4\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8046)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(298))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(447))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(894))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1341))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2682))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\)\(^{\oplus 2}\)