Space of modular forms of level 1890, weight 2, and Character 1890.bf

• Label: 1890.2.bf
• Level: $1890$
• Weight: $2$
• Character orbit: 1890.bf
• Rep. character: $\chi_{1890}(629,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $864$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(864\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

	Total	New	Old
Modular forms	912	96	816
Cusp forms	816	96	720
Eisenstein series	96	0	96

Trace form

\( 96 q - 48 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1890.2.bf.a	$1890$	$2$	1890.bf	315.z	$6$	$8$	$4$	$15.092$	8.0.856615824.2	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1890.2.bf.b	$1890$	$2$	1890.bf	315.z	$6$	$8$	$4$	$15.092$	8.0.856615824.2	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1890.2.bf.c	$1890$	$2$	1890.bf	315.z	$6$	$8$	$4$	$15.092$	8.0.856615824.2	None		$2$	$0$	\(4\)	\(0\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{2}-\beta _{2}q^{4}+(-2-\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1890.2.bf.d	$1890$	$2$	1890.bf	315.z	$6$	$8$	$4$	$15.092$	8.0.856615824.2	None		$2$	$0$	\(4\)	\(0\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{2})q^{2}-\beta _{2}q^{4}+(2+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
1890.2.bf.e	$1890$	$2$	1890.bf	315.z	$6$	$32$	$16$	$15.092$		None		$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1890.2.bf.f	$1890$	$2$	1890.bf	315.z	$6$	$32$	$16$	$15.092$		None		$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)