Space of modular forms of level 6078, weight 2, and trivial character

• Label: 6078.2.a
• Level: $6078$
• Weight: $2$
• Character orbit: 6078.a
• Rep. character: $\chi_{6078}(1,\cdot)$
• Character field: $\Q$
• Dimension: $169$
• Newform subspaces: $11$
• Sturm bound: $2028$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 6078 = 2 \cdot 3 \cdot 1013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6078.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2028\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6078))\).

	Total	New	Old
Modular forms	1018	169	849
Cusp forms	1011	169	842
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.

\(2\)	\(3\)	\(1013\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(23\)
\(+\)	\(+\)	\(-\)	$-$	\(19\)
\(+\)	\(-\)	\(+\)	$-$	\(28\)
\(+\)	\(-\)	\(-\)	$+$	\(15\)
\(-\)	\(+\)	\(+\)	$-$	\(19\)
\(-\)	\(+\)	\(-\)	$+$	\(23\)
\(-\)	\(-\)	\(+\)	$+$	\(15\)
\(-\)	\(-\)	\(-\)	$-$	\(27\)
Plus space			\(+\)	\(76\)
Minus space			\(-\)	\(93\)

Trace form

\( 169 q - q^{2} + q^{3} + 169 q^{4} - 6 q^{5} - q^{6} - 4 q^{7} - q^{8} + 169 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6078))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	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	1013
6078.2.a.a	$6078$	$2$	6078.a	1.a	$1$	$1$	$1$	$48.533$	\(\Q\)	None	✓	✓	6078.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
6078.2.a.b	$6078$	$2$	6078.a	1.a	$1$	$1$	$1$	$48.533$	\(\Q\)	None	✓	✓	6078.2.a.b	$1$	$1$	\(1\)	\(-1\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-2q^{7}+\cdots\)
6078.2.a.c	$6078$	$2$	6078.a	1.a	$1$	$2$	$2$	$48.533$	\(\Q(\sqrt{5}) \)	None	✓	✓	6078.2.a.c	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-2\beta q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots\)
6078.2.a.d	$6078$	$2$	6078.a	1.a	$1$	$14$	$14$	$48.533$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	6078.2.a.d	$1$	$1$	\(-14\)	\(14\)	\(-2\)	\(-12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
6078.2.a.e	$6078$	$2$	6078.a	1.a	$1$	$15$	$15$	$48.533$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	6078.2.a.e	$1$	$1$	\(15\)	\(15\)	\(-14\)	\(-18\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{8})q^{5}+q^{6}+\cdots\)
6078.2.a.f	$6078$	$2$	6078.a	1.a	$1$	$17$	$17$	$48.533$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	6078.2.a.f	$1$	$0$	\(-17\)	\(-17\)	\(10\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
6078.2.a.g	$6078$	$2$	6078.a	1.a	$1$	$19$	$19$	$48.533$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	6078.2.a.g	$1$	$0$	\(19\)	\(-19\)	\(8\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{6}q^{7}+\cdots\)
6078.2.a.h	$6078$	$2$	6078.a	1.a	$1$	$22$	$22$	$48.533$		None	✓	✓	6078.2.a.h	$1$	$1$	\(22\)	\(-22\)	\(-5\)	\(-7\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
6078.2.a.i	$6078$	$2$	6078.a	1.a	$1$	$23$	$23$	$48.533$		None	✓	✓	6078.2.a.i	$1$	$1$	\(-23\)	\(-23\)	\(-7\)	\(3\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6078.2.a.j	$6078$	$2$	6078.a	1.a	$1$	$27$	$27$	$48.533$		None	✓	✓	6078.2.a.j	$1$	$0$	\(27\)	\(27\)	\(9\)	\(17\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
6078.2.a.k	$6078$	$2$	6078.a	1.a	$1$	$28$	$28$	$48.533$		None	✓	✓	6078.2.a.k	$1$	$0$	\(-28\)	\(28\)	\(1\)	\(13\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6078))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6078)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1013))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2026))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3039))\)\(^{\oplus 2}\)