Space of modular forms of level 3042, weight 2, and Character 3042.b

• Label: 3042.2.b
• Level: $3042$
• Weight: $2$
• Character orbit: 3042.b
• Rep. character: $\chi_{3042}(1351,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $18$
• Sturm bound: $1092$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3042.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1092\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3042, [\chi])\).

	Total	New	Old
Modular forms	602	66	536
Cusp forms	490	66	424
Eisenstein series	112	0	112

Trace form

66 * q - 66 * q^4 - 2 * q^10 - 4 * q^14 + 66 * q^16 + 4 * q^17 - 2 * q^22 - 60 * q^25 - 26 * q^29 + 28 * q^35 + 26 * q^38 + 2 * q^40 - 2 * q^43 - 78 * q^49 - 30 * q^53 + 8 * q^55 + 4 * q^56 + 18 * q^61 - 24 * q^62 - 66 * q^64 - 4 * q^68 - 14 * q^74 - 12 * q^77 - 12 * q^79 + 16 * q^82 + 2 * q^88 - 16 * q^94 - 20 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(3042, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3042.2.b.a	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					26.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+3 i q^{5}+i q^{7}-i q^{8}+\cdots\)
3042.2.b.b	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					234.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+2 i q^{5}+2 i q^{7}-i q^{8}+\cdots\)
3042.2.b.c	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					234.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+2 i q^{5}-2 i q^{7}-i q^{8}+\cdots\)
3042.2.b.d	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					78.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+i q^{5}+2 i q^{7}-i q^{8}+\cdots\)
3042.2.b.e	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					26.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+i q^{5}-4 i q^{7}+i q^{8}+\cdots\)
3042.2.b.f	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					26.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+i q^{5}-i q^{7}+i q^{8}+\cdots\)
3042.2.b.g	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					78.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+2 i q^{5}+4 i q^{7}+i q^{8}+\cdots\)
3042.2.b.h	$3042$	$2$	3042.b	13.b	$2$	$2$	$2$	$24.290$	\(\Q(\sqrt{-1}) \)	None					78.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+3 i q^{5}+2 i q^{7}+i q^{8}+\cdots\)
3042.2.b.i	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	\(\Q(\zeta_{12})\)	None					78.2.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}-q^{4}+(\beta_{2}+2\beta_1)q^{5}+\cdots\)
3042.2.b.j	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	\(\Q(i, \sqrt{10})\)	None					234.2.h.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots\)
3042.2.b.k	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	\(\Q(i, \sqrt{10})\)	None					234.2.h.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
3042.2.b.l	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	\(\Q(\zeta_{12})\)	None					78.2.i.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}-q^{4}-\beta_{2} q^{5}+(\beta_{2}-3\beta_1)q^{7}+\cdots\)
3042.2.b.m	$3042$	$2$	3042.b	13.b	$2$	$4$	$4$	$24.290$	\(\Q(\zeta_{12})\)	None					234.2.l.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}-q^{4}+3\beta_1 q^{5}+\beta_1 q^{8}+\cdots\)
3042.2.b.n	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None					338.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{4}+2\beta _{1}q^{5}+(-2\beta _{3}-2\beta _{5})q^{7}+\cdots\)
3042.2.b.o	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None					1014.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{4}+(-2\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3042.2.b.p	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None		✓			3042.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{4}+\beta _{1}q^{5}+(-3\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
3042.2.b.q	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None		✓			3042.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{4}+\beta _{1}q^{5}+(3\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
3042.2.b.r	$3042$	$2$	3042.b	13.b	$2$	$6$	$6$	$24.290$	6.0.153664.1	None					1014.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{4}+(\beta _{1}+\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3042, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3042, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1521, [\chi])\)\(^{\oplus 2}\)