Space of modular forms of level 5700, weight 2, and Character 5700.f

• Label: 5700.2.f
• Level: $5700$
• Weight: $2$
• Character orbit: 5700.f
• Rep. character: $\chi_{5700}(3649,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $18$
• Sturm bound: $2400$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5700.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(2400\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5700, [\chi])\).

	Total	New	Old
Modular forms	1236	56	1180
Cusp forms	1164	56	1108
Eisenstein series	72	0	72

Trace form

\( 56 q - 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5700, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5700.2.f.a	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-5q^{11}+6iq^{13}+\cdots\)
5700.2.f.b	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-4q^{11}-4iq^{17}+\cdots\)
5700.2.f.c	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-4q^{11}+6iq^{17}+\cdots\)
5700.2.f.d	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-2iq^{13}+\cdots\)
5700.2.f.e	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-4iq^{13}-q^{19}+\cdots\)
5700.2.f.f	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}+4iq^{13}+6iq^{17}+\cdots\)
5700.2.f.g	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-4iq^{13}+2iq^{17}+\cdots\)
5700.2.f.h	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{7}-q^{9}-2iq^{17}+q^{19}+\cdots\)
5700.2.f.i	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}+2q^{11}+6iq^{13}+\cdots\)
5700.2.f.j	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+5iq^{7}-q^{9}+2q^{11}-2iq^{13}+\cdots\)
5700.2.f.k	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-q^{9}+2q^{11}+2iq^{13}-6iq^{17}+\cdots\)
5700.2.f.l	$5700$	$2$	5700.f	5.b	$2$	$2$	$2$	$45.515$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}+4q^{11}+2iq^{17}+\cdots\)
5700.2.f.m	$5700$	$2$	5700.f	5.b	$2$	$4$	$4$	$45.515$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(-1-\beta _{3})q^{11}+\cdots\)
5700.2.f.n	$5700$	$2$	5700.f	5.b	$2$	$4$	$4$	$45.515$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)
5700.2.f.o	$5700$	$2$	5700.f	5.b	$2$	$4$	$4$	$45.515$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+4\beta _{1}q^{7}-q^{9}+(1+\beta _{3})q^{11}+\cdots\)
5700.2.f.p	$5700$	$2$	5700.f	5.b	$2$	$6$	$6$	$45.515$	6.0.37161216.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{5}q^{7}-q^{9}+(-1-\beta _{3}+\cdots)q^{11}+\cdots\)
5700.2.f.q	$5700$	$2$	5700.f	5.b	$2$	$6$	$6$	$45.515$	6.0.5089536.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{1}-\beta _{4})q^{7}-q^{9}+(2-\beta _{2}+\cdots)q^{11}+\cdots\)
5700.2.f.r	$5700$	$2$	5700.f	5.b	$2$	$8$	$8$	$45.515$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{3}+\beta _{5})q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2850, [\chi])\)\(^{\oplus 2}\)