Space of modular forms of level 1725, weight 2, and Character 1725.b

• Label: 1725.2.b
• Level: $1725$
• Weight: $2$
• Character orbit: 1725.b
• Rep. character: $\chi_{1725}(1174,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $21$
• Sturm bound: $480$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1725.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(480\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1725, [\chi])\).

	Total	New	Old
Modular forms	252	64	188
Cusp forms	228	64	164
Eisenstein series	24	0	24

Trace form

\( 64 q - 60 q^{4} - 4 q^{6} - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1725, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1725.2.b.a	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+5iq^{7}+\cdots\)
1725.2.b.b	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+3iq^{7}+\cdots\)
1725.2.b.c	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots\)
1725.2.b.d	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}+5iq^{7}+\cdots\)
1725.2.b.e	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{7}+\cdots\)
1725.2.b.f	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}+4iq^{7}+\cdots\)
1725.2.b.g	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}-2iq^{7}+\cdots\)
1725.2.b.h	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}-3iq^{7}+\cdots\)
1725.2.b.i	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2q^{4}-iq^{7}-q^{9}-6q^{11}+\cdots\)
1725.2.b.j	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{4}+3iq^{7}-q^{9}-4q^{11}+\cdots\)
1725.2.b.k	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{4}-3iq^{7}-q^{9}+2q^{11}+\cdots\)
1725.2.b.l	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2q^{4}-iq^{7}-q^{9}+4q^{11}+\cdots\)
1725.2.b.m	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}-4q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots\)
1725.2.b.n	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{21})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.b.o	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1725.2.b.p	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+(-2+\cdots)q^{4}+\cdots\)
1725.2.b.q	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.b.r	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
1725.2.b.s	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+(\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1725.2.b.t	$1725$	$2$	1725.b	5.b	$2$	$6$	$6$	$13.774$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots\)
1725.2.b.u	$1725$	$2$	1725.b	5.b	$2$	$6$	$6$	$13.774$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{1})q^{4}+\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1725, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1725, [\chi]) \cong \)