Space of modular forms of level 3375, weight 1, and Character 3375.m

• Label: 3375.1.m
• Level: $3375$
• Weight: $1$
• Character orbit: 3375.m
• Rep. character: $\chi_{3375}(674,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $450$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3375 = 3^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3375.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(450\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3375, [\chi])\).

	Total	New	Old
Modular forms	136	16	120
Cusp forms	16	16	0
Eisenstein series	120	0	120

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

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

Trace form

\( 16 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3375, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3375.1.m.a	$3375$	$1$	3375.m	75.h	$10$	$8$	$2$	$1.684$	\(\Q(\zeta_{20})\)	$A_{5}$	None	None		$4$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1+\zeta_{20}^{2})q^{2}+(1-\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{4}+\cdots\)
3375.1.m.b	$3375$	$1$	3375.m	75.h	$10$	$8$	$2$	$1.684$	\(\Q(\zeta_{20})\)	$A_{5}$	None	None		$4$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{20}^{2})q^{2}+(1-\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{4}+\cdots\)