Space of modular forms of level 228, weight 2, and Character 228.f

• Label: 228.2.f
• Level: $228$
• Weight: $2$
• Character orbit: 228.f
• Rep. character: $\chi_{228}(151,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(228, [\chi])\).

	Total	New	Old
Modular forms	44	20	24
Cusp forms	36	20	16
Eisenstein series	8	0	8

Trace form

\( 20 q + 4 q^{4} - 4 q^{6} + 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(228, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
228.2.f.a	$228$	$2$	228.f	76.d	$2$	$10$	$10$	$1.821$	10.0.\(\cdots\).1	None		$2$	$0$	\(-2\)	\(10\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
228.2.f.b	$228$	$2$	228.f	76.d	$2$	$10$	$10$	$1.821$	10.0.\(\cdots\).1	None		$2$	$0$	\(2\)	\(-10\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(228, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(228, [\chi]) \cong \)