Space of modular forms of level 1575, weight 2, and Character 1575.bk

• Label: 1575.2.bk
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.bk
• Rep. character: $\chi_{1575}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $100$
• Newform subspaces: $9$
• Sturm bound: $480$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(480\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

	Total	New	Old
Modular forms	528	100	428
Cusp forms	432	100	332
Eisenstein series	96	0	96

Trace form

\( 100 q + 48 q^{4} + 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1575.2.bk.a	$1575$	$2$	1575.bk	21.g	$6$	$4$	$2$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\beta _{2})q^{4}+(-1-2\beta _{2})q^{7}+\cdots\)
1575.2.bk.b	$1575$	$2$	1575.bk	21.g	$6$	$4$	$2$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\beta _{2})q^{4}+(1+2\beta _{2})q^{7}+\beta _{1}q^{11}+\cdots\)
1575.2.bk.c	$1575$	$2$	1575.bk	21.g	$6$	$4$	$2$	$12.576$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+3\beta _{2})q^{7}-2\beta _{3}q^{8}+\cdots\)
1575.2.bk.d	$1575$	$2$	1575.bk	21.g	$6$	$8$	$4$	$12.576$	8.0.796594176.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{2}q^{4}+(\beta _{6}+\beta _{7})q^{7}+2\beta _{3}q^{11}+\cdots\)
1575.2.bk.e	$1575$	$2$	1575.bk	21.g	$6$	$12$	$6$	$12.576$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1575.2.bk.f	$1575$	$2$	1575.bk	21.g	$6$	$12$	$6$	$12.576$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{4}-\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1575.2.bk.g	$1575$	$2$	1575.bk	21.g	$6$	$16$	$8$	$12.576$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{8}-\beta _{9}+\beta _{15})q^{2}+(2-2\beta _{3}+\cdots)q^{4}+\cdots\)
1575.2.bk.h	$1575$	$2$	1575.bk	21.g	$6$	$16$	$8$	$12.576$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{8}-\beta _{9}+\beta _{15})q^{2}+(2-2\beta _{3}+\cdots)q^{4}+\cdots\)
1575.2.bk.i	$1575$	$2$	1575.bk	21.g	$6$	$24$	$12$	$12.576$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)