Space of modular forms of level 1805, weight 2, and Character 1805.b

• Label: 1805.2.b
• Level: $1805$
• Weight: $2$
• Character orbit: 1805.b
• Rep. character: $\chi_{1805}(1084,\cdot)$
• Character field: $\Q$
• Dimension: $154$
• Newform subspaces: $13$
• Sturm bound: $380$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(380\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1805, [\chi])\).

	Total	New	Old
Modular forms	210	188	22
Cusp forms	170	154	16
Eisenstein series	40	34	6

Trace form

\( 154 q - 138 q^{4} + 4 q^{5} - 118 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1805, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1805.2.b.a	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2q^{4}+(-1+i)q^{5}+2iq^{7}+\cdots\)
1805.2.b.b	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2q^{4}+(-1-i)q^{5}-2iq^{7}+\cdots\)
1805.2.b.c	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots\)
1805.2.b.d	$1805$	$2$	1805.b	5.b	$2$	$2$	$2$	$14.413$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{4}+(-1+\beta )q^{5}+(-1+2\beta )q^{7}+\cdots\)
1805.2.b.e	$1805$	$2$	1805.b	5.b	$2$	$6$	$6$	$14.413$	6.0.16516096.1	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
1805.2.b.f	$1805$	$2$	1805.b	5.b	$2$	$6$	$6$	$14.413$	6.0.4227136.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
1805.2.b.g	$1805$	$2$	1805.b	5.b	$2$	$6$	$6$	$14.413$	6.0.4227136.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
1805.2.b.h	$1805$	$2$	1805.b	5.b	$2$	$8$	$8$	$14.413$	8.0.\(\cdots\).2	\(\Q(\sqrt{-95}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1805.2.b.i	$1805$	$2$	1805.b	5.b	$2$	$16$	$16$	$14.413$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
1805.2.b.j	$1805$	$2$	1805.b	5.b	$2$	$16$	$16$	$14.413$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
1805.2.b.k	$1805$	$2$	1805.b	5.b	$2$	$24$	$24$	$14.413$		None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1805.2.b.l	$1805$	$2$	1805.b	5.b	$2$	$24$	$24$	$14.413$		None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1805.2.b.m	$1805$	$2$	1805.b	5.b	$2$	$40$	$40$	$14.413$		None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1805, [\chi]) \cong \)