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

• Label: 1890.2.d
• Level: $1890$
• Weight: $2$
• Character orbit: 1890.d
• Rep. character: $\chi_{1890}(1889,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $6$
• Sturm bound: $864$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(864\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(11\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	456	64	392
Cusp forms	408	64	344
Eisenstein series	48	0	48

Trace form

\( 64 q + 64 q^{4} + O(q^{10}) \)

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.d.a	$1890$	$2$	1890.d	105.g	$2$	$8$	$8$	$15.092$	8.0.303595776.1	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(-\beta _{3}-\beta _{5}+\beta _{7})q^{5}+\cdots\)
1890.2.d.b	$1890$	$2$	1890.d	105.g	$2$	$8$	$8$	$15.092$	8.0.\(\cdots\).2	None		$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1890.2.d.c	$1890$	$2$	1890.d	105.g	$2$	$8$	$8$	$15.092$	8.0.\(\cdots\).2	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(\beta _{1}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots\)
1890.2.d.d	$1890$	$2$	1890.d	105.g	$2$	$8$	$8$	$15.092$	8.0.303595776.1	None		$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(\beta _{1}+\beta _{3}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1890.2.d.e	$1890$	$2$	1890.d	105.g	$2$	$16$	$16$	$15.092$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{15}q^{5}-\beta _{6}q^{7}-q^{8}+\cdots\)
1890.2.d.f	$1890$	$2$	1890.d	105.g	$2$	$16$	$16$	$15.092$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{8}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)