Space of modular forms of level 1575, weight 1, and Character 1575.e

• Label: 1575.1.e
• Level: $1575$
• Weight: $1$
• Character orbit: 1575.e
• Rep. character: $\chi_{1575}(874,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1575.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1575, [\chi])\).

	Total	New	Old
Modular forms	38	10	28
Cusp forms	14	8	6
Eisenstein series	24	2	22

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 6 q^{4} + 2 q^{11} - 2 q^{14} + 4 q^{16} - 2 q^{29} - 10 q^{46} - 8 q^{49} - 2 q^{56} + 4 q^{64} + 2 q^{71} + 2 q^{74} + 2 q^{79} - 2 q^{86}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1575.1.e.a	$1575$	$1$	1575.e	35.c	$2$	$2$	$2$	$0.786$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None					175.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{2}-i q^{7}-i q^{8}+q^{11}-q^{14}+\cdots\)
1575.1.e.b	$1575$	$1$	1575.e	35.c	$2$	$2$	$2$	$0.786$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{21}) \)					63.1.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}-i q^{7}+q^{16}-i q^{28}-2 i q^{37}+\cdots\)
1575.1.e.c	$1575$	$1$	1575.e	35.c	$2$	$4$	$4$	$0.786$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-7}) \)	None		✓	✓		1575.1.h.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1575, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)