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

• Label: 1530.2.c
• Level: $1530$
• Weight: $2$
• Character orbit: 1530.c
• Rep. character: $\chi_{1530}(271,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $9$
• Sturm bound: $648$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(648\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(47\)

Dimensions

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

	Total	New	Old
Modular forms	340	30	310
Cusp forms	308	30	278
Eisenstein series	32	0	32

Trace form

30 * q - 2 * q^2 + 30 * q^4 - 2 * q^8 - 12 * q^13 + 30 * q^16 - 6 * q^17 + 4 * q^19 - 30 * q^25 - 8 * q^26 - 2 * q^32 + 6 * q^34 + 12 * q^35 + 24 * q^38 + 24 * q^43 - 16 * q^47 - 22 * q^49 + 2 * q^50 - 12 * q^52 + 20 * q^53 + 8 * q^55 + 20 * q^59 + 30 * q^64 + 24 * q^67 - 6 * q^68 + 4 * q^70 + 4 * q^76 + 32 * q^77 - 32 * q^83 + 8 * q^85 + 32 * q^86 + 40 * q^89 + 20 * q^94 + 26 * q^98

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.c.a	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None					170.2.b.c	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-i q^{5}+2 i q^{7}-q^{8}+\cdots\)
1530.2.c.b	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None					170.2.b.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+i q^{5}+4 i q^{7}-q^{8}+\cdots\)
1530.2.c.c	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None					510.2.c.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-i q^{5}+2 i q^{7}-q^{8}+\cdots\)
1530.2.c.d	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None					170.2.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-i q^{5}+q^{8}-i q^{10}+\cdots\)
1530.2.c.e	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	\(\Q(\sqrt{-1}) \)	None					510.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-i q^{5}+q^{8}-i q^{10}+\cdots\)
1530.2.c.f	$1530$	$2$	1530.c	17.b	$2$	$4$	$4$	$12.217$	\(\Q(\zeta_{8})\)	None					510.2.c.d	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta_1 q^{5}+(\beta_{2}+2\beta_1)q^{7}+\cdots\)
1530.2.c.g	$1530$	$2$	1530.c	17.b	$2$	$4$	$4$	$12.217$	\(\Q(i, \sqrt{13})\)	None					510.2.c.c	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
1530.2.c.h	$1530$	$2$	1530.c	17.b	$2$	$6$	$6$	$12.217$	6.0.5089536.1	None		✓			1530.2.c.h	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
1530.2.c.i	$1530$	$2$	1530.c	17.b	$2$	$6$	$6$	$12.217$	6.0.5089536.1	None		✓			1530.2.c.h	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)