Space of modular forms of level 3100, weight 2, and Character 3100.c

• Label: 3100.2.c
• Level: $3100$
• Weight: $2$
• Character orbit: 3100.c
• Rep. character: $\chi_{3100}(249,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $9$
• Sturm bound: $960$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3100.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3100, [\chi])\).

	Total	New	Old
Modular forms	498	44	454
Cusp forms	462	44	418
Eisenstein series	36	0	36

Trace form

\( 44 q - 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3100.2.c.a	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	\(\Q(\sqrt{-1}) \)	None					620.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-2iq^{7}-6q^{9}+2q^{11}-2iq^{13}+\cdots\)
3100.2.c.b	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	\(\Q(\sqrt{-1}) \)	None					124.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{7}-q^{9}-6q^{11}-2iq^{13}+\cdots\)
3100.2.c.c	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	\(\Q(\sqrt{-1}) \)	None					620.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}+2q^{9}+2iq^{13}+3iq^{17}+\cdots\)
3100.2.c.d	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	\(\Q(\sqrt{-1}) \)	None					620.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{7}+3q^{9}-4q^{11}+2iq^{13}+2iq^{23}+\cdots\)
3100.2.c.e	$3100$	$2$	3100.c	5.b	$2$	$2$	$2$	$24.754$	\(\Q(\sqrt{-1}) \)	None					124.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3iq^{7}+3q^{9}+6q^{11}-4iq^{13}+\cdots\)
3100.2.c.f	$3100$	$2$	3100.c	5.b	$2$	$6$	$6$	$24.754$	6.0.9144576.1	None					620.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{3})q^{3}+(\beta _{1}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\)
3100.2.c.g	$3100$	$2$	3100.c	5.b	$2$	$8$	$8$	$24.754$	8.0.\(\cdots\).1	None					620.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots\)
3100.2.c.h	$3100$	$2$	3100.c	5.b	$2$	$10$	$10$	$24.754$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			3100.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}+(\beta _{2}-\beta _{6}+\beta _{8})q^{7}+\cdots\)
3100.2.c.i	$3100$	$2$	3100.c	5.b	$2$	$10$	$10$	$24.754$	10.0.\(\cdots\).1	None		✓			3100.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{8})q^{3}+(\beta _{6}+\beta _{7})q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)