Space of modular forms of level 1800, weight 2, and Character 1800.f

• Label: 1800.2.f
• Level: $1800$
• Weight: $2$
• Character orbit: 1800.f
• Rep. character: $\chi_{1800}(649,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $11$
• Sturm bound: $720$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(720\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

	Total	New	Old
Modular forms	408	22	386
Cusp forms	312	22	290
Eisenstein series	96	0	96

Trace form

\( 22 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1800.2.f.a	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}-4q^{11}-iq^{13}+iq^{17}+\cdots\)
1800.2.f.b	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-4q^{11}+iq^{13}-4iq^{17}+\cdots\)
1800.2.f.c	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{11}-iq^{13}+iq^{17}+4q^{19}+\cdots\)
1800.2.f.d	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-2q^{11}-2iq^{13}+iq^{17}+\cdots\)
1800.2.f.e	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{7}-2q^{11}+3iq^{13}-6iq^{17}+\cdots\)
1800.2.f.f	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}-q^{11}-4iq^{13}-5iq^{17}+\cdots\)
1800.2.f.g	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}+3iq^{13}+iq^{17}-4q^{19}+\cdots\)
1800.2.f.h	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+2q^{11}-2iq^{13}-iq^{17}+\cdots\)
1800.2.f.i	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+4q^{11}+iq^{13}+4iq^{17}+\cdots\)
1800.2.f.j	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{11}-3iq^{13}+3iq^{17}+4q^{19}+\cdots\)
1800.2.f.k	$1800$	$2$	1800.f	5.b	$2$	$2$	$2$	$14.373$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{7}+6q^{11}-3iq^{13}-2iq^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)