Space of modular forms of level 3100, weight 3, and Character 3100.d

• Label: 3100.3.d
• Level: $3100$
• Weight: $3$
• Character orbit: 3100.d
• Rep. character: $\chi_{3100}(1301,\cdot)$
• Character field: $\Q$
• Dimension: $102$
• Newform subspaces: $8$
• Sturm bound: $1440$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	3100.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1440\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3100, [\chi])\).

	Total	New	Old
Modular forms	978	102	876
Cusp forms	942	102	840
Eisenstein series	36	0	36

Trace form

\( 102 q + 2 q^{7} - 322 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(3100, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3100.3.d.a	$3100$	$3$	3100.d	31.b	$2$	$2$	$2$	$84.469$	\(\Q(\sqrt{-3}) \)	None			124.3.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}+10q^{7}-3q^{9}-5\zeta_{6}q^{11}+\cdots\)
3100.3.d.b	$3100$	$3$	3100.d	31.b	$2$	$4$	$4$	$84.469$	4.0.63368.1	None			124.3.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{7}+(-1-2\beta _{3})q^{9}+\cdots\)
3100.3.d.c	$3100$	$3$	3100.d	31.b	$2$	$4$	$4$	$84.469$	\(\Q(\sqrt{-5}, \sqrt{-93})\)	\(\Q(\sqrt{-155}) \)			620.3.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+(-2^{4}+\beta _{3})q^{9}-3\beta _{2}q^{13}+\cdots\)
3100.3.d.d	$3100$	$3$	3100.d	31.b	$2$	$4$	$4$	$84.469$	\(\Q(\sqrt{-15}, \sqrt{-31})\)	\(\Q(\sqrt{-155}) \)			620.3.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+(-2-\beta _{3})q^{9}+(-\beta _{1}+5\beta _{2}+\cdots)q^{13}+\cdots\)
3100.3.d.e	$3100$	$3$	3100.d	31.b	$2$	$20$	$20$	$84.469$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None			620.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{23}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{6})q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots\)
3100.3.d.f	$3100$	$3$	3100.d	31.b	$2$	$22$	$22$	$84.469$		None		✓	3100.3.d.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$
3100.3.d.g	$3100$	$3$	3100.d	31.b	$2$	$22$	$22$	$84.469$		None		✓	3100.3.d.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{2}]$
3100.3.d.h	$3100$	$3$	3100.d	31.b	$2$	$24$	$24$	$84.469$		None			620.3.f.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(3100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)