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

• Label: 1575.2.g
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.g
• Rep. character: $\chi_{1575}(1574,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $5$
• Sturm bound: $480$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(480\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(59\)

Dimensions

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

	Total	New	Old
Modular forms	264	48	216
Cusp forms	216	48	168
Eisenstein series	48	0	48

Trace form

\( 48 q + 48 q^{4} + 48 q^{16} + 96 q^{46} - 36 q^{49} + 192 q^{64} - 48 q^{79} - 12 q^{91}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1575.2.g.a	$1575$	$2$	1575.g	105.g	$2$	$8$	$8$	$12.576$	\(\Q(\zeta_{24})\)	None					315.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{2}+\beta_{3} q^{4}+(\beta_{6}-\beta_{5}-\beta_1)q^{7}+\cdots\)
1575.2.g.b	$1575$	$2$	1575.g	105.g	$2$	$8$	$8$	$12.576$	\(\Q(\zeta_{24})\)	None		✓			1575.2.b.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{6} q^{2}+(-\beta_{4}+\beta_1)q^{7}-2\beta_{6} q^{8}+\cdots\)
1575.2.g.c	$1575$	$2$	1575.g	105.g	$2$	$8$	$8$	$12.576$	\(\Q(\zeta_{24})\)	None					315.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{2}+\beta_{3} q^{4}+(-\beta_{6}+\beta_{5}+\beta_1)q^{7}+\cdots\)
1575.2.g.d	$1575$	$2$	1575.g	105.g	$2$	$8$	$8$	$12.576$	\(\Q(i, \sqrt{2}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)					63.2.c.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{6}q^{2}+(2+\beta _{5})q^{4}-\beta _{1}q^{7}+(\beta _{3}+\cdots)q^{8}+\cdots\)
1575.2.g.e	$1575$	$2$	1575.g	105.g	$2$	$16$	$16$	$12.576$	\(\Q(i, \sqrt{2}, \sqrt{3}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		✓	✓		1575.2.b.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{8}\cdot 5^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{10}q^{2}+(2+\beta _{4})q^{4}-\beta _{9}q^{7}+(\beta _{3}+\cdots)q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)