Space of modular forms of level 3850, weight 2, and Character 3850.c

• Label: 3850.2.c
• Level: $3850$
• Weight: $2$
• Character orbit: 3850.c
• Rep. character: $\chi_{3850}(1849,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $29$
• Sturm bound: $1440$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(1440\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(3\), \(13\), \(17\), \(19\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

	Total	New	Old
Modular forms	744	92	652
Cusp forms	696	92	604
Eisenstein series	48	0	48

Trace form

92 * q - 92 * q^4 - 108 * q^9 + 4 * q^11 - 8 * q^14 + 92 * q^16 + 24 * q^26 - 40 * q^29 + 24 * q^31 - 40 * q^34 + 108 * q^36 + 48 * q^39 - 40 * q^41 - 4 * q^44 - 92 * q^49 + 16 * q^51 + 8 * q^56 + 88 * q^59 + 8 * q^61 - 92 * q^64 + 16 * q^69 - 8 * q^71 - 8 * q^74 - 32 * q^79 + 140 * q^81 + 24 * q^86 - 80 * q^89 + 8 * q^91 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3850.2.c.a	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.b	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.c	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-i q^{7}+\cdots\)
3850.2.c.d	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					154.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.e	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None		✓			3850.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+i q^{7}+\cdots\)
3850.2.c.f	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None		✓			3850.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
3850.2.c.g	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None		✓			3850.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
3850.2.c.h	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+i q^{7}-i q^{8}+3 q^{9}+\cdots\)
3850.2.c.i	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None		✓			3850.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-i q^{7}+i q^{8}+3 q^{9}+\cdots\)
3850.2.c.j	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					154.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-i q^{7}+i q^{8}+3 q^{9}+\cdots\)
3850.2.c.k	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None		✓			3850.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+i q^{7}+i q^{8}+3 q^{9}+\cdots\)
3850.2.c.l	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					154.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-i q^{7}-i q^{8}+3 q^{9}+\cdots\)
3850.2.c.m	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-i q^{7}-i q^{8}+3 q^{9}+\cdots\)
3850.2.c.n	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None		✓			3850.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}-i q^{7}+\cdots\)
3850.2.c.o	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}+i q^{7}+\cdots\)
3850.2.c.p	$3850$	$2$	3850.c	5.b	$2$	$2$	$2$	$30.742$	\(\Q(\sqrt{-1}) \)	None					770.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-i q^{7}+\cdots\)
3850.2.c.q	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(i, \sqrt{5})\)	None					154.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
3850.2.c.r	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(\zeta_{12})\)	None		✓			3850.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
3850.2.c.s	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(\zeta_{12})\)	None					770.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
3850.2.c.t	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(i, \sqrt{10})\)	None		✓			3850.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.u	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(\zeta_{8})\)	None					770.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+\beta_{2} q^{3}-q^{4}+\beta_{3} q^{6}+\cdots\)
3850.2.c.v	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(i, \sqrt{7})\)	None		✓			3850.2.a.bh	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.w	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(\zeta_{8})\)	None		✓			3850.2.a.bg	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+\beta_{2} q^{3}-q^{4}+\beta_{3} q^{6}+\cdots\)
3850.2.c.x	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(\zeta_{12})\)	None					770.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
3850.2.c.y	$3850$	$2$	3850.c	5.b	$2$	$4$	$4$	$30.742$	\(\Q(i, \sqrt{33})\)	None					770.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2\beta _{1}q^{3}-q^{4}+2q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.z	$3850$	$2$	3850.c	5.b	$2$	$6$	$6$	$30.742$	6.0.3182656.1	None					770.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{4}q^{7}+\cdots\)
3850.2.c.ba	$3850$	$2$	3850.c	5.b	$2$	$6$	$6$	$30.742$	6.0.399424.1	None					770.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.c.bb	$3850$	$2$	3850.c	5.b	$2$	$6$	$6$	$30.742$	6.0.399424.1	None		✓			3850.2.a.bs	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
3850.2.c.bc	$3850$	$2$	3850.c	5.b	$2$	$6$	$6$	$30.742$	6.0.3534400.1	None		✓			3850.2.a.br	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)