Space of modular forms of level 1530, weight 2, and Character 1530.d

• Label: 1530.2.d
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.d
• Rep. character: $\chi_{1530}(919,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $10$
• Sturm bound: $648$
• Trace bound: $11$

Defining parameters

Level:	$N$	$=$	$1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1530.d (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$10$
Sturm bound:			$648$
Trace bound:			$11$
Distinguishing $T_p$:			$7$, $11$, $29$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1530, [\chi])$.

	Total	New	Old
Modular forms	340	40	300
Cusp forms	308	40	268
Eisenstein series	32	0	32

Trace form

40 * q - 40 * q^4 - 4 * q^5 + 4 * q^10 - 8 * q^11 + 8 * q^14 + 40 * q^16 - 4 * q^19 + 4 * q^20 - 12 * q^25 - 4 * q^26 - 8 * q^29 + 32 * q^31 - 4 * q^34 - 20 * q^35 - 4 * q^40 + 8 * q^41 + 8 * q^44 - 8 * q^46 - 32 * q^49 + 4 * q^50 - 8 * q^55 - 8 * q^56 - 12 * q^59 + 8 * q^61 - 40 * q^64 - 8 * q^65 + 4 * q^70 + 48 * q^71 + 8 * q^74 + 4 * q^76 - 40 * q^79 - 4 * q^80 - 4 * q^85 + 24 * q^86 + 12 * q^89 + 56 * q^91 + 20 * q^94 - 16 * q^95

Decomposition of $S_{2}^{\mathrm{new}}(1530, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1530.2.d.a	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1})$	None		✓			1530.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i-2)q^{5}+i q^{8}+\cdots$
1530.2.d.b	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1})$	None					170.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(-2 i-1)q^{5}+i q^{8}+\cdots$
1530.2.d.c	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1})$	None					510.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i+2)q^{5}+4 i q^{7}+\cdots$
1530.2.d.d	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1})$	None		✓			1530.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i+2)q^{5}+i q^{8}+\cdots$
1530.2.d.e	$1530$	$2$	1530.d	5.b	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{6})$	None					510.2.d.c	$2$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
1530.2.d.f	$1530$	$2$	1530.d	5.b	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{5})$	None					510.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1530.2.d.g	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.5161984.1	None					170.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1530.2.d.h	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		✓			1530.2.d.h	$2$	$0$	$0$	$0$	$-2$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$
1530.2.d.i	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.5161984.1	None					510.2.d.d	$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$
1530.2.d.j	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		✓			1530.2.d.h	$2$	$0$	$0$	$0$	$2$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(1530, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(1530, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(30, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(45, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(85, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(90, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(170, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(255, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(510, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(765, [\chi])$$^{\oplus 2}$