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 - 8 * q^14 + 68 * q^16 + 4 * q^19 - 4 * q^21 + 12 * q^24 + 8 * q^26 + 24 * q^29 - 28 * q^31 - 8 * q^34 + 60 * q^36 + 20 * q^39 - 64 * q^41 + 24 * q^44 - 8 * q^46 - 28 * q^49 + 4 * q^54 + 48 * q^56 - 48 * q^59 - 52 * q^61 - 44 * q^64 + 32 * q^66 + 8 * q^69 + 56 * q^71 + 112 * q^74 + 8 * q^76 - 8 * q^79 + 64 * q^81 - 32 * q^84 + 96 * q^86 + 72 * q^89 + 20 * q^91 + 40 * q^94 - 28 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	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					345.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}+5 i q^{7}+\cdots\)
1725.2.b.b	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None					345.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}+3 i q^{7}+\cdots\)
1725.2.b.c	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None					345.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}-4 i q^{7}+\cdots\)
1725.2.b.d	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		✓			1725.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}+5 i q^{7}+\cdots\)
1725.2.b.e	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		✓			1725.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+3 i q^{7}+\cdots\)
1725.2.b.f	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None					345.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+4 i q^{7}+\cdots\)
1725.2.b.g	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None					69.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}-2 i q^{7}+\cdots\)
1725.2.b.h	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		✓			1725.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}-3 i q^{7}+\cdots\)
1725.2.b.i	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		✓			1725.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}-i q^{7}-q^{9}-6 q^{11}+\cdots\)
1725.2.b.j	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None					345.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{4}+3 i q^{7}-q^{9}-4 q^{11}+\cdots\)
1725.2.b.k	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None		✓			1725.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{4}-3 i q^{7}-q^{9}+2 q^{11}+\cdots\)
1725.2.b.l	$1725$	$2$	1725.b	5.b	$2$	$2$	$2$	$13.774$	\(\Q(\sqrt{-1}) \)	None					345.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}-i q^{7}-q^{9}+4 q^{11}+\cdots\)
1725.2.b.m	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{6})\)	None					345.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}-4q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots\)
1725.2.b.n	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{21})\)	None		✓			1725.2.a.x	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.b.o	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{5})\)	None					69.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1725.2.b.p	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(\zeta_{12})\)	None					345.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{2}-\beta_1 q^{3}+(2\beta_{3}-2)q^{4}+\cdots\)
1725.2.b.q	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{5})\)	None		✓			1725.2.a.v	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.b.r	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(i, \sqrt{13})\)	None		✓			1725.2.a.w	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
1725.2.b.s	$1725$	$2$	1725.b	5.b	$2$	$4$	$4$	$13.774$	\(\Q(\zeta_{8})\)	None					345.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{2}-\beta_1 q^{3}-\beta_{3} q^{6}+(2\beta_{2}+\beta_1)q^{7}+\cdots\)
1725.2.b.t	$1725$	$2$	1725.b	5.b	$2$	$6$	$6$	$13.774$	6.0.3356224.1	None		✓			1725.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots\)
1725.2.b.u	$1725$	$2$	1725.b	5.b	$2$	$6$	$6$	$13.774$	6.0.399424.1	None					345.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{2}q^{3}+(-1-\beta _{1})q^{4}+\beta _{3}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1725, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)