Space of modular forms of level 3800, weight 2, and Character 3800.d

• Label: 3800.2.d
• Level: $3800$
• Weight: $2$
• Character orbit: 3800.d
• Rep. character: $\chi_{3800}(3649,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $17$
• Sturm bound: $1200$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3800.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1200\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3800, [\chi])\).

	Total	New	Old
Modular forms	624	82	542
Cusp forms	576	82	494
Eisenstein series	48	0	48

Trace form

\( 82 q - 78 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3800, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3800.2.d.a	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+iq^{7}-6q^{9}+4q^{11}+iq^{13}+\cdots\)
3800.2.d.b	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-q^{9}-4q^{11}-2iq^{13}-iq^{17}+\cdots\)
3800.2.d.c	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-2iq^{7}-q^{9}-4q^{11}-3iq^{17}+\cdots\)
3800.2.d.d	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-3iq^{7}-q^{9}-3q^{11}+4iq^{13}+\cdots\)
3800.2.d.e	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}+4q^{11}+2iq^{13}+\cdots\)
3800.2.d.f	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-3iq^{7}+2q^{9}+2q^{11}+iq^{13}+\cdots\)
3800.2.d.g	$3800$	$2$	3800.d	5.b	$2$	$2$	$2$	$30.343$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{9}-4q^{11}-3iq^{13}+3iq^{17}+\cdots\)
3800.2.d.h	$3800$	$2$	3800.d	5.b	$2$	$4$	$4$	$30.343$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}^{3})q^{9}+2q^{11}+\cdots\)
3800.2.d.i	$3800$	$2$	3800.d	5.b	$2$	$4$	$4$	$30.343$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{3}+2\zeta_{8}^{2}q^{7}+q^{9}+(2-\zeta_{8}^{3})q^{11}+\cdots\)
3800.2.d.j	$3800$	$2$	3800.d	5.b	$2$	$6$	$6$	$30.343$	6.0.59105344.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}-\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots\)
3800.2.d.k	$3800$	$2$	3800.d	5.b	$2$	$6$	$6$	$30.343$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{3}-\beta _{5})q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
3800.2.d.l	$3800$	$2$	3800.d	5.b	$2$	$6$	$6$	$30.343$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{5}q^{7}+(-1+\beta _{1})q^{9}+(\beta _{2}+\cdots)q^{13}+\cdots\)
3800.2.d.m	$3800$	$2$	3800.d	5.b	$2$	$6$	$6$	$30.343$	6.0.4227136.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+\beta _{3}q^{7}+(-\beta _{2}-\beta _{5})q^{9}+\cdots\)
3800.2.d.n	$3800$	$2$	3800.d	5.b	$2$	$6$	$6$	$30.343$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{4}-\beta _{5})q^{7}-\beta _{1}q^{9}+2\beta _{1}q^{11}+\cdots\)
3800.2.d.o	$3800$	$2$	3800.d	5.b	$2$	$6$	$6$	$30.343$	6.0.419904.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{5})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3800.2.d.p	$3800$	$2$	3800.d	5.b	$2$	$12$	$12$	$30.343$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{9}q^{7}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
3800.2.d.q	$3800$	$2$	3800.d	5.b	$2$	$12$	$12$	$30.343$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{8})q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)