Space of modular forms of level 300, weight 1, and Character 300.l

• Label: 300.1.l
• Level: $300$
• Weight: $1$
• Character orbit: 300.l
• Rep. character: $\chi_{300}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(300, [\chi])\).

	Total	New	Old
Modular forms	28	12	16
Cusp forms	4	4	0
Eisenstein series	24	8	16

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

\( 4 q - 4 q^{6} - 4 q^{16} + 4 q^{36} + 8 q^{46} - 8 q^{61} - 4 q^{81} + 4 q^{96}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(300, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{3}) \)		✓	✓	✓	300.1.l.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)