Space of modular forms of level 300, weight 2, and Character 300.e

• Label: 300.2.e
• Level: $300$
• Weight: $2$
• Character orbit: 300.e
• Rep. character: $\chi_{300}(251,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(12\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(300, [\chi])\).

	Total	New	Old
Modular forms	72	44	28
Cusp forms	48	32	16
Eisenstein series	24	12	12

Trace form

\( 32 q + 2 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(300, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
300.2.e.a	$300$	$2$	300.e	12.b	$2$	$4$	$4$	$2.396$	\(\Q(\sqrt{3}, \sqrt{-5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
300.2.e.b	$300$	$2$	300.e	12.b	$2$	$4$	$4$	$2.396$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.2.e.c	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.342102016.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.e.d	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.4521217600.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
300.2.e.e	$300$	$2$	300.e	12.b	$2$	$8$	$8$	$2.396$	8.0.4521217600.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(300, [\chi]) \cong \)