Space of modular forms of level 1512, weight 2, and Character 1512.r

• Label: 1512.2.r
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.r
• Rep. character: $\chi_{1512}(505,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $36$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.r (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

	Total	New	Old
Modular forms	624	36	588
Cusp forms	528	36	492
Eisenstein series	96	0	96

Trace form

36 * q - 14 * q^11 - 12 * q^17 - 12 * q^19 - 4 * q^23 - 18 * q^25 + 12 * q^29 + 24 * q^35 + 6 * q^41 + 6 * q^43 + 12 * q^47 - 18 * q^49 - 48 * q^53 - 14 * q^59 + 16 * q^65 + 6 * q^67 - 24 * q^71 + 36 * q^73 + 8 * q^77 - 16 * q^83 - 24 * q^85 + 48 * q^89 - 12 * q^95 - 42 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1512.2.r.a	$1512$	$2$	1512.r	9.c	$3$	$2$	$1$	$12.073$	\(\Q(\sqrt{-3}) \)	None					504.2.r.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1512.2.r.b	$1512$	$2$	1512.r	9.c	$3$	$2$	$1$	$12.073$	\(\Q(\sqrt{-3}) \)	None					504.2.r.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1512.2.r.c	$1512$	$2$	1512.r	9.c	$3$	$6$	$3$	$12.073$	\(\Q(\zeta_{18})\)	None					504.2.r.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{2}-\beta_1)q^{5}+(\beta_1-1)q^{7}+(-2\beta_{5}+\beta_{3}-\beta_{2})q^{11}+\cdots\)
1512.2.r.d	$1512$	$2$	1512.r	9.c	$3$	$8$	$4$	$12.073$	8.0.508277025.1	None					504.2.r.d	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}+\beta _{4}-\beta _{5}+\beta _{7})q^{5}+\beta _{5}q^{7}+\cdots\)
1512.2.r.e	$1512$	$2$	1512.r	9.c	$3$	$8$	$4$	$12.073$	8.0.2091141441.1	None					504.2.r.e	$2$	$0$	\(0\)	\(0\)	\(3\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{2}+\beta _{3})q^{5}-\beta _{3}q^{7}+(\beta _{1}+2\beta _{3}+\cdots)q^{11}+\cdots\)
1512.2.r.f	$1512$	$2$	1512.r	9.c	$3$	$10$	$5$	$12.073$	10.0.\(\cdots\).1	None			✓		504.2.r.f	$2$	$0$	\(0\)	\(0\)	\(3\)	\(5\)	$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{7})q^{5}-\beta _{1}q^{7}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)