Space of modular forms of level 1170, weight 2, and Character 1170.bp

• Label: 1170.2.bp
• Level: $1170$
• Weight: $2$
• Character orbit: 1170.bp
• Rep. character: $\chi_{1170}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $68$
• Newform subspaces: $9$
• Sturm bound: $504$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bp (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(504\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

	Total	New	Old
Modular forms	536	68	468
Cusp forms	472	68	404
Eisenstein series	64	0	64

Trace form

68 * q + 34 * q^4 + 10 * q^11 - 12 * q^14 - 34 * q^16 + 22 * q^19 - 16 * q^25 + 4 * q^29 - 24 * q^31 + 24 * q^34 + 26 * q^35 - 20 * q^41 + 20 * q^44 - 8 * q^46 + 24 * q^49 - 12 * q^55 - 6 * q^56 + 32 * q^59 + 44 * q^61 - 68 * q^64 + 14 * q^65 + 24 * q^70 + 32 * q^71 + 14 * q^74 - 22 * q^76 + 40 * q^79 + 58 * q^85 + 24 * q^86 - 26 * q^89 + 18 * q^91 - 30 * q^94 + 32 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1170.2.bp.a	$1170$	$2$	1170.bp	65.n	$6$	$4$	$2$	$9.342$	\(\Q(\zeta_{12})\)	None					390.2.y.f	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bp.b	$1170$	$2$	1170.bp	65.n	$6$	$4$	$2$	$9.342$	\(\Q(\zeta_{12})\)	None					390.2.y.e	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bp.c	$1170$	$2$	1170.bp	65.n	$6$	$4$	$2$	$9.342$	\(\Q(\zeta_{12})\)	None					390.2.y.d	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bp.d	$1170$	$2$	1170.bp	65.n	$6$	$4$	$2$	$9.342$	\(\Q(\zeta_{12})\)	None					390.2.y.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bp.e	$1170$	$2$	1170.bp	65.n	$6$	$4$	$2$	$9.342$	\(\Q(\zeta_{12})\)	None					390.2.y.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1170.2.bp.f	$1170$	$2$	1170.bp	65.n	$6$	$4$	$2$	$9.342$	\(\Q(\zeta_{12})\)	None					390.2.y.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1170.2.bp.g	$1170$	$2$	1170.bp	65.n	$6$	$8$	$4$	$9.342$	8.0.303595776.1	None					390.2.y.g	$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}-\beta _{4}q^{4}+(1-\beta _{6})q^{5}+(2\beta _{2}+\cdots)q^{7}+\cdots\)
1170.2.bp.h	$1170$	$2$	1170.bp	65.n	$6$	$12$	$6$	$9.342$	12.0.\(\cdots\).1	None					130.2.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+\beta _{8}q^{4}+(\beta _{1}-\beta _{7})q^{5}+(2\beta _{3}+\cdots)q^{7}+\cdots\)
1170.2.bp.i	$1170$	$2$	1170.bp	65.n	$6$	$24$	$12$	$9.342$		None		✓	✓		1170.2.bp.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)