Space of modular forms of level 6016, weight 2, and trivial character

• Label: 6016.2.a
• Level: $6016$
• Weight: $2$
• Character orbit: 6016.a
• Rep. character: $\chi_{6016}(1,\cdot)$
• Character field: $\Q$
• Dimension: $184$
• Newform subspaces: $20$
• Sturm bound: $1536$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 6016 = 2^{7} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6016.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1536\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6016))\).

	Total	New	Old
Modular forms	784	184	600
Cusp forms	753	184	569
Eisenstein series	31	0	31

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

\(2\)	\(47\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(43\)
\(+\)	\(-\)	$-$	\(51\)
\(-\)	\(+\)	$-$	\(49\)
\(-\)	\(-\)	$+$	\(41\)
Plus space		\(+\)	\(84\)
Minus space		\(-\)	\(100\)

Trace form

\( 184 q + 184 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6016))\) 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	47
6016.2.a.a	$6016$	$2$	6016.a	1.a	$1$	$1$	$1$	$48.038$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}-4q^{13}+2q^{17}+8q^{19}+\cdots\)
6016.2.a.b	$6016$	$2$	6016.a	1.a	$1$	$1$	$1$	$48.038$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+4q^{13}+2q^{17}+8q^{19}+\cdots\)
6016.2.a.c	$6016$	$2$	6016.a	1.a	$1$	$1$	$1$	$48.038$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}-4q^{13}+2q^{17}-8q^{19}+\cdots\)
6016.2.a.d	$6016$	$2$	6016.a	1.a	$1$	$1$	$1$	$48.038$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+4q^{13}+2q^{17}-8q^{19}+\cdots\)
6016.2.a.e	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
6016.2.a.f	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{6})q^{7}+\cdots\)
6016.2.a.g	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
6016.2.a.h	$6016$	$2$	6016.a	1.a	$1$	$8$	$8$	$48.038$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(1+\beta _{6})q^{7}+\cdots\)
6016.2.a.i	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.j	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.k	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.l	$6016$	$2$	6016.a	1.a	$1$	$10$	$10$	$48.038$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
6016.2.a.m	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-6\)	\(2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{8}q^{5}+\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.n	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(6\)	\(-2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{8}q^{5}-\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.o	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(-6\)	\(-2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.p	$6016$	$2$	6016.a	1.a	$1$	$13$	$13$	$48.038$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(6\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.q	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(-2\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.r	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(6\)	\(2\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.s	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-6\)	\(2\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6016.2.a.t	$6016$	$2$	6016.a	1.a	$1$	$14$	$14$	$48.038$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(6\)	\(-2\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{12}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(94))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(376))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(752))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3008))\)\(^{\oplus 2}\)