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 - 104 * q^10 + 24 * q^12 - 96 * q^14 + 1248 * q^16 + 192 * q^17 + 200 * q^22 - 8 * q^23 - 1658 * q^25 - 54 * q^27 - 56 * q^29 - 120 * q^30 + 1560 * q^35 - 2808 * q^36 - 704 * q^38 + 416 * q^40 + 168 * q^42 - 1064 * q^43 - 96 * q^48 - 3330 * q^49 + 348 * q^51 - 528 * q^53 - 336 * q^55 + 384 * q^56 - 2352 * q^61 - 2464 * q^62 - 4992 * q^64 + 1152 * q^66 - 768 * q^68 - 1992 * q^69 + 704 * q^74 + 1674 * q^75 + 1256 * q^77 + 3300 * q^79 + 6318 * q^81 + 224 * q^82 - 2736 * q^87 - 800 * q^88 - 936 * q^90 + 32 * q^92 + 1088 * q^94 - 224 * q^95

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	Twist minimal	Largest	Maximal	Minimal twist	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					78.4.a.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3 q^{3}-4 q^{4}+8\beta q^{5}-3\beta q^{6}+\cdots\)
1014.4.b.b	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					78.4.e.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-3 q^{3}-4 q^{4}+7 i q^{5}+\cdots\)
1014.4.b.c	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					78.4.a.e	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3 q^{3}-4 q^{4}+3\beta q^{5}-3\beta q^{6}+\cdots\)
1014.4.b.d	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					6.4.a.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-3 q^{3}-4 q^{4}+3\beta q^{5}+3\beta q^{6}+\cdots\)
1014.4.b.e	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					78.4.a.d	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-3 q^{3}-4 q^{4}+10\beta q^{5}+\cdots\)
1014.4.b.f	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					78.4.a.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+3 q^{3}-4 q^{4}+8\beta q^{5}+3\beta q^{6}+\cdots\)
1014.4.b.g	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					78.4.a.f	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+3 q^{3}-4 q^{4}+2\beta q^{5}+3\beta q^{6}+\cdots\)
1014.4.b.h	$1014$	$4$	1014.b	13.b	$2$	$2$	$2$	$59.828$	\(\Q(\sqrt{-1}) \)	None					78.4.a.c	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+3 q^{3}-4 q^{4}+5\beta q^{5}-3\beta q^{6}+\cdots\)
1014.4.b.i	$1014$	$4$	1014.b	13.b	$2$	$4$	$4$	$59.828$	\(\Q(i, \sqrt{61})\)	None					78.4.e.c	$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{2}-3q^{3}-4q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.j	$1014$	$4$	1014.b	13.b	$2$	$4$	$4$	$59.828$	\(\Q(i, \sqrt{673})\)	None					78.4.e.b	$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}-6\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.k	$1014$	$4$	1014.b	13.b	$2$	$4$	$4$	$59.828$	\(\Q(\zeta_{12})\)	None					78.4.i.a	$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta_1 q^{2}+3 q^{3}-4 q^{4}+(\beta_{2}+6\beta_1)q^{5}+\cdots\)
1014.4.b.l	$1014$	$4$	1014.b	13.b	$2$	$6$	$6$	$59.828$	6.0.153664.1	None		✓			1014.4.a.t	$2$	$0$	\(0\)	\(-18\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{5}q^{2}-3q^{3}-4q^{4}+(-2\beta _{1}-3\beta _{3}+\cdots)q^{5}+\cdots\)
1014.4.b.m	$1014$	$4$	1014.b	13.b	$2$	$6$	$6$	$59.828$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					78.4.e.d	$2$	$0$	\(0\)	\(18\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}+4\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.n	$1014$	$4$	1014.b	13.b	$2$	$6$	$6$	$59.828$	6.0.153664.1	None		✓			1014.4.a.v	$2$	$0$	\(0\)	\(18\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{5}q^{2}+3q^{3}-4q^{4}+(3\beta _{1}+5\beta _{3}+\cdots)q^{5}+\cdots\)
1014.4.b.o	$1014$	$4$	1014.b	13.b	$2$	$8$	$8$	$59.828$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					78.4.i.b	$2$	$0$	\(0\)	\(-24\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-3q^{3}-4q^{4}+(3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.p	$1014$	$4$	1014.b	13.b	$2$	$12$	$12$	$59.828$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1014.4.a.bb	$2$	$0$	\(0\)	\(-36\)	\(0\)	\(0\)	$13^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{7}q^{2}-3q^{3}-4q^{4}+(-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
1014.4.b.q	$1014$	$4$	1014.b	13.b	$2$	$12$	$12$	$59.828$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1014.4.a.bc	$2$	$0$	\(0\)	\(36\)	\(0\)	\(0\)	$13^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{3}q^{2}+3q^{3}-4q^{4}+\beta _{8}q^{5}-6\beta _{3}q^{6}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)