Space of modular forms of level 2475, weight 1, and Character 2475.m

• Label: 2475.1.m
• Level: $2475$
• Weight: $1$
• Character orbit: 2475.m
• Rep. character: $\chi_{2475}(593,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $360$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2475.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 165 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(360\)
Trace bound:			\(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2475, [\chi])\).

	Total	New	Old
Modular forms	88	16	72
Cusp forms	40	16	24
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2475.1.m.a	$2475$	$1$	2475.m	165.l	$4$	$8$	$4$	$1.235$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-55}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$		\(q+(-\zeta_{16}+\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)
2475.1.m.b	$2475$	$1$	2475.m	165.l	$4$	$8$	$4$	$1.235$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-55}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$		\(q+(\zeta_{16}-\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2475, [\chi]) \cong \)