Space of modular forms of level 2925, weight 1, and Character 2925.bi

• Label: 2925.1.bi
• Level: $2925$
• Weight: $1$
• Character orbit: 2925.bi
• Rep. character: $\chi_{2925}(1676,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $420$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2925.bi (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(420\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2925, [\chi])\).

	Total	New	Old
Modular forms	28	16	12
Cusp forms	4	4	0
Eisenstein series	24	12	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{4} + 4 q^{9} - 2 q^{16} + 6 q^{29} + 2 q^{36} - 2 q^{39} - 2 q^{49} + 4 q^{61} - 4 q^{64} - 6 q^{69} - 2 q^{79} + 4 q^{81}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2925, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2925.1.bi.a	$2925$	$1$	2925.bi	117.n	$6$	$2$	$1$	$1.460$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{13}) \)		✓			2925.1.bi.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{3}+\zeta_{6}q^{4}+q^{9}-\zeta_{6}q^{12}+\zeta_{6}q^{13}+\cdots\)
2925.1.bi.b	$2925$	$1$	2925.bi	117.n	$6$	$2$	$1$	$1.460$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{13}) \)		✓			2925.1.bi.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+q^{3}+\zeta_{6}q^{4}+q^{9}+\zeta_{6}q^{12}-\zeta_{6}q^{13}+\cdots\)