Space of modular forms of level 1014, weight 4, and Character 1014.b

• Label: 1014.4.b
• Level: $1014$
• Weight: $4$
• Character orbit: 1014.b
• Rep. character: $\chi_{1014}(337,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $17$
• Sturm bound: $728$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(728\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1014, [\chi])\).

	Total	New	Old
Modular forms	574	78	496
Cusp forms	518	78	440
Eisenstein series	56	0	56

Trace form

\( 78 q - 6 q^{3} - 312 q^{4} + 702 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1014.4.b.a	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-3q^{3}-4q^{4}+8iq^{5}-3iq^{6}+\cdots\)
1014.4.b.b	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-3q^{3}-4q^{4}+7iq^{5}-6iq^{6}+\cdots\)
1014.4.b.c	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-3q^{3}-4q^{4}+3iq^{5}-3iq^{6}+\cdots\)
1014.4.b.d	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-3q^{3}-4q^{4}+3iq^{5}+3iq^{6}+\cdots\)
1014.4.b.e	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-3q^{3}-4q^{4}+10iq^{5}+3iq^{6}+\cdots\)
1014.4.b.f	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3q^{3}-4q^{4}+8iq^{5}+3iq^{6}+\cdots\)
1014.4.b.g	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3q^{3}-4q^{4}+2iq^{5}+3iq^{6}+\cdots\)
1014.4.b.h	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+3q^{3}-4q^{4}+5iq^{5}-3iq^{6}+\cdots\)
1014.4.b.i	$1014$	$4$	1014.b	13.b	$2$	$4$	$4$	$59.828$	\(\Q(i, \sqrt{61})\)	None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{2}-3q^{3}-4q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.j	$1014$	$4$	1014.b	13.b	$2$	$4$	$4$	$59.828$	\(\Q(i, \sqrt{673})\)	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}-6\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.k	$1014$	$4$	1014.b	13.b	$2$	$4$	$4$	$59.828$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\zeta_{12}q^{2}+3q^{3}-4q^{4}+(6\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1014.4.b.l	$1014$	$4$	1014.b	13.b	$2$	$6$	$6$	$59.828$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-18\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{5}q^{2}-3q^{3}-4q^{4}+(-2\beta _{1}-3\beta _{3}+\cdots)q^{5}+\cdots\)
1014.4.b.m	$1014$	$4$	1014.b	13.b	$2$	$6$	$6$	$59.828$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(18\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}+4\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.n	$1014$	$4$	1014.b	13.b	$2$	$6$	$6$	$59.828$	6.0.153664.1	None		$2$	$0$	\(0\)	\(18\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{5}q^{2}+3q^{3}-4q^{4}+(3\beta _{1}+5\beta _{3}+\cdots)q^{5}+\cdots\)
1014.4.b.o	$1014$	$4$	1014.b	13.b	$2$	$8$	$8$	$59.828$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-24\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-3q^{3}-4q^{4}+(3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.p	$1014$	$4$	1014.b	13.b	$2$	$12$	$12$	$59.828$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-36\)	\(0\)	\(0\)	$13^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{7}q^{2}-3q^{3}-4q^{4}+(-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
1014.4.b.q	$1014$	$4$	1014.b	13.b	$2$	$12$	$12$	$59.828$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(36\)	\(0\)	\(0\)	$13^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{3}q^{2}+3q^{3}-4q^{4}+\beta _{8}q^{5}-6\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)