Space of modular forms of level 2205, weight 2, and Character 2205.d

• Label: 2205.2.d
• Level: $2205$
• Weight: $2$
• Character orbit: 2205.d
• Rep. character: $\chi_{2205}(1324,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $20$
• Sturm bound: $672$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(672\)
Trace bound:			\(16\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

	Total	New	Old
Modular forms	368	108	260
Cusp forms	304	98	206
Eisenstein series	64	10	54

Trace form

\( 98 q - 94 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2205.2.d.a	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-3q^{4}+\beta q^{5}-\beta q^{8}-5q^{10}+\cdots\)
2205.2.d.b	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+(-2+i)q^{5}+(-2+\cdots)q^{10}+\cdots\)
2205.2.d.c	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-2-i)q^{5}+3iq^{8}+\cdots\)
2205.2.d.d	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(-1-2i)q^{5}+3iq^{8}+\cdots\)
2205.2.d.e	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(1+2i)q^{5}+3iq^{8}+\cdots\)
2205.2.d.f	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(1+2i)q^{5}+3iq^{8}+\cdots\)
2205.2.d.g	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+(2-i)q^{5}+3iq^{8}+(1+\cdots)q^{10}+\cdots\)
2205.2.d.h	$2205$	$2$	2205.d	5.b	$2$	$2$	$2$	$17.607$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-35}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{4}+\beta q^{5}+3q^{11}+3\beta q^{13}+4q^{16}+\cdots\)
2205.2.d.i	$2205$	$2$	2205.d	5.b	$2$	$4$	$4$	$17.607$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-4q^{4}+(-\beta _{1}+\beta _{2})q^{5}-2\beta _{3}q^{8}+\cdots\)
2205.2.d.j	$2205$	$2$	2205.d	5.b	$2$	$4$	$4$	$17.607$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+\beta _{2}q^{8}-\beta _{3}q^{10}+\cdots\)
2205.2.d.k	$2205$	$2$	2205.d	5.b	$2$	$4$	$4$	$17.607$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+q^{4}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+3\zeta_{8}^{2}q^{8}+\cdots\)
2205.2.d.l	$2205$	$2$	2205.d	5.b	$2$	$6$	$6$	$17.607$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
2205.2.d.m	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.309760000.3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-2-\beta _{1})q^{4}+\beta _{2}q^{5}+(-\beta _{5}+\cdots)q^{8}+\cdots\)
2205.2.d.n	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.3317760000.3	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+(-2+\beta _{2})q^{4}+\beta _{6}q^{5}+(4\beta _{3}+\cdots)q^{8}+\cdots\)
2205.2.d.o	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots\)
2205.2.d.p	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(-1-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2205.2.d.q	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.\(\cdots\).4	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{4}+\beta _{7}q^{5}+\beta _{2}q^{8}+(-\beta _{3}+\cdots)q^{10}+\cdots\)
2205.2.d.r	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(-1-\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
2205.2.d.s	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
2205.2.d.t	$2205$	$2$	2205.d	5.b	$2$	$8$	$8$	$17.607$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}^{3}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{4}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \)