Space of modular forms of level 6040, weight 2, and trivial character

• Label: 6040.2.a
• Level: $6040$
• Weight: $2$
• Character orbit: 6040.a
• Rep. character: $\chi_{6040}(1,\cdot)$
• Character field: $\Q$
• Dimension: $150$
• Newform subspaces: $19$
• Sturm bound: $1824$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6040.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1824\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6040))\).

	Total	New	Old
Modular forms	920	150	770
Cusp forms	905	150	755
Eisenstein series	15	0	15

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

\(2\)	\(5\)	\(151\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(24\)
\(+\)	\(+\)	\(-\)	$-$	\(14\)
\(+\)	\(-\)	\(+\)	$-$	\(16\)
\(+\)	\(-\)	\(-\)	$+$	\(20\)
\(-\)	\(+\)	\(+\)	$-$	\(23\)
\(-\)	\(+\)	\(-\)	$+$	\(15\)
\(-\)	\(-\)	\(+\)	$+$	\(12\)
\(-\)	\(-\)	\(-\)	$-$	\(26\)
Plus space			\(+\)	\(71\)
Minus space			\(-\)	\(79\)

Trace form

\( 150 q - 4 q^{3} - 2 q^{5} + 158 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6040))\) 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	5	151
6040.2.a.a	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-3\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-4q^{7}+6q^{9}-q^{11}+\cdots\)
6040.2.a.b	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
6040.2.a.c	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}-2q^{9}-5q^{11}+\cdots\)
6040.2.a.d	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
6040.2.a.e	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}+5q^{11}-q^{13}+\cdots\)
6040.2.a.f	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
6040.2.a.g	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots\)
6040.2.a.h	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}-2q^{9}-3q^{11}+\cdots\)
6040.2.a.i	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}-2q^{9}+4q^{11}+\cdots\)
6040.2.a.j	$6040$	$2$	6040.a	1.a	$1$	$1$	$1$	$48.230$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
6040.2.a.k	$6040$	$2$	6040.a	1.a	$1$	$2$	$2$	$48.230$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
6040.2.a.l	$6040$	$2$	6040.a	1.a	$1$	$9$	$9$	$48.230$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(9\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{7}q^{3}+q^{5}+(\beta _{1}+\beta _{4})q^{7}-\beta _{5}q^{9}+\cdots\)
6040.2.a.m	$6040$	$2$	6040.a	1.a	$1$	$12$	$12$	$48.230$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-12\)	\(5\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+\beta _{9}q^{7}+(1-\beta _{3}+\beta _{10}+\cdots)q^{9}+\cdots\)
6040.2.a.n	$6040$	$2$	6040.a	1.a	$1$	$13$	$13$	$48.230$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-13\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}-\beta _{7}q^{7}+\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)
6040.2.a.o	$6040$	$2$	6040.a	1.a	$1$	$15$	$15$	$48.230$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(5\)	\(15\)	\(7\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-\beta _{4}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6040.2.a.p	$6040$	$2$	6040.a	1.a	$1$	$19$	$19$	$48.230$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(19\)	\(-8\)		$+$	$-$	$-$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6040.2.a.q	$6040$	$2$	6040.a	1.a	$1$	$23$	$23$	$48.230$		None	✓	$1$	$1$	\(0\)	\(-4\)	\(-23\)	\(-9\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6040.2.a.r	$6040$	$2$	6040.a	1.a	$1$	$23$	$23$	$48.230$		None	✓	$1$	$0$	\(0\)	\(2\)	\(-23\)	\(3\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
6040.2.a.s	$6040$	$2$	6040.a	1.a	$1$	$24$	$24$	$48.230$		None	✓	$1$	$0$	\(0\)	\(2\)	\(24\)	\(3\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(302))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(604))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(755))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1510))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3020))\)\(^{\oplus 2}\)