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

• Label: 300.1.b
• Level: $300$
• Weight: $1$
• Character orbit: 300.b
• Rep. character: $\chi_{300}(149,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
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	20	2	18
Cusp forms	2	2	0
Eisenstein series	18	0	18

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{9} + 2 q^{19} - 2 q^{21} - 2 q^{31} + 2 q^{39} - 2 q^{61} - 4 q^{79} + 2 q^{81} + 2 q^{91}+O(q^{100}) \)

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.b.a	$300$	$1$	300.b	15.d	$2$	$2$	$2$	$0.150$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	300.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{3}-i q^{7}-q^{9}+i q^{13}+q^{19}+\cdots\)