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

• Label: 1512.2.bl
• Level: $1512$
• Weight: $2$
• Character orbit: 1512.bl
• Rep. character: $\chi_{1512}(593,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(19\)
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	64	560
Cusp forms	528	64	464
Eisenstein series	96	0	96

Trace form

\( 64 q + 4 q^{7} - 6 q^{19} - 42 q^{25} + 42 q^{31} - 2 q^{37} - 40 q^{43} - 16 q^{49} + 14 q^{67} + 30 q^{73} - 2 q^{79} + 16 q^{85} - 12 q^{91}+O(q^{100}) \)

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.bl.a	$1512$	$2$	1512.bl	21.g	$6$	$16$	$8$	$12.073$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1512.2.bl.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{5}-\beta _{2}q^{7}+(-\beta _{7}-\beta _{12})q^{11}+\cdots\)
1512.2.bl.b	$1512$	$2$	1512.bl	21.g	$6$	$16$	$8$	$12.073$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1512.2.bl.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{13}-\beta _{14})q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1512.2.bl.c	$1512$	$2$	1512.bl	21.g	$6$	$16$	$8$	$12.073$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1512.2.bl.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{14}q^{5}+(\beta _{4}-\beta _{5}-\beta _{7}+\beta _{9})q^{7}+\cdots\)
1512.2.bl.d	$1512$	$2$	1512.bl	21.g	$6$	$16$	$8$	$12.073$	16.0.\(\cdots\).1	None		✓			1512.2.bl.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{16}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{10})q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{6}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)