Space of modular forms of level 1925, weight 1, and Character 1925.ct

• Label: 1925.1.ct
• Level: $1925$
• Weight: $1$
• Character orbit: 1925.ct
• Rep. character: $\chi_{1925}(318,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1925.ct (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 385 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1925, [\chi])\).

	Total	New	Old
Modular forms	64	32	32
Cusp forms	16	16	0
Eisenstein series	48	16	32

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

\( 16 q - 16 q^{36} + 8 q^{56} - 16 q^{71} + 8 q^{81} + 8 q^{86} + 8 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1925, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1925.1.ct.a	$1925$	$1$	1925.ct	385.af	$12$	$8$	$2$	$0.961$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-55}) \)	None		✓			1925.1.ct.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{2}+\zeta_{24}^{3}q^{7}-\zeta_{24}^{9}q^{8}+\cdots\)
1925.1.ct.b	$1925$	$1$	1925.ct	385.af	$12$	$8$	$2$	$0.961$	\(\Q(\zeta_{24})\)	$D_{6}$	\(\Q(\sqrt{-55}) \)	None		✓			1925.1.ct.b	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)