Space of modular forms of level 300, weight 4, and Character 300.d

• Label: 300.4.d
• Level: $300$
• Weight: $4$
• Character orbit: 300.d
• Rep. character: $\chi_{300}(49,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	300.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(300, [\chi])\).

	Total	New	Old
Modular forms	198	10	188
Cusp forms	162	10	152
Eisenstein series	36	0	36

Trace form

\( 10 q - 90 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(300, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.4.d.a	$300$	$4$	300.d	5.b	$2$	$2$	$2$	$17.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+7iq^{7}-9q^{9}-54q^{11}+\cdots\)
300.4.d.b	$300$	$4$	300.d	5.b	$2$	$2$	$2$	$17.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+28iq^{7}-9q^{9}-24q^{11}+\cdots\)
300.4.d.c	$300$	$4$	300.d	5.b	$2$	$2$	$2$	$17.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+13iq^{7}-9q^{9}+6q^{11}+\cdots\)
300.4.d.d	$300$	$4$	300.d	5.b	$2$	$2$	$2$	$17.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+2^{5}iq^{7}-9q^{9}+6^{2}q^{11}+\cdots\)
300.4.d.e	$300$	$4$	300.d	5.b	$2$	$2$	$2$	$17.701$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{3}+8iq^{7}-9q^{9}+6^{2}q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)