Space of modular forms of level 3120, weight 2, and Character 3120.l

• Label: 3120.2.l
• Level: $3120$
• Weight: $2$
• Character orbit: 3120.l
• Rep. character: $\chi_{3120}(1249,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $17$
• Sturm bound: $1344$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3120.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1344\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

	Total	New	Old
Modular forms	696	72	624
Cusp forms	648	72	576
Eisenstein series	48	0	48

Trace form

\( 72 q - 72 q^{9} - 32 q^{19} - 8 q^{25} - 16 q^{31} + 48 q^{35} + 8 q^{39} - 56 q^{49} + 8 q^{51} + 16 q^{55} - 16 q^{61} + 16 q^{69} - 8 q^{75} - 8 q^{79} + 72 q^{81} - 16 q^{85} + 24 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3120.2.l.a	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					390.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-i-2)q^{5}-q^{9}+6 q^{11}+\cdots\)
3120.2.l.b	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					1560.2.l.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i-1)q^{5}+5 i q^{7}+\cdots\)
3120.2.l.c	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					195.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i-1)q^{5}+i q^{7}-q^{9}+\cdots\)
3120.2.l.d	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					780.2.h.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(2 i-1)q^{5}+i q^{7}-q^{9}+\cdots\)
3120.2.l.e	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					1560.2.l.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-2 i+1)q^{5}+i q^{7}-q^{9}+\cdots\)
3120.2.l.f	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					780.2.h.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i+1)q^{5}+3 i q^{7}+\cdots\)
3120.2.l.g	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					390.2.e.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-i+2)q^{5}+2 i q^{7}-q^{9}+\cdots\)
3120.2.l.h	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					390.2.e.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i+2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
3120.2.l.i	$3120$	$2$	3120.l	5.b	$2$	$2$	$2$	$24.913$	\(\Q(\sqrt{-1}) \)	None					390.2.e.d	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i+2)q^{5}+4 i q^{7}-q^{9}+\cdots\)
3120.2.l.j	$3120$	$2$	3120.l	5.b	$2$	$4$	$4$	$24.913$	\(\Q(i, \sqrt{6})\)	None					780.2.h.c	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}-2\beta _{2}q^{7}+\cdots\)
3120.2.l.k	$3120$	$2$	3120.l	5.b	$2$	$4$	$4$	$24.913$	\(\Q(i, \sqrt{5})\)	None					390.2.e.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3120.2.l.l	$3120$	$2$	3120.l	5.b	$2$	$4$	$4$	$24.913$	\(\Q(\zeta_{8})\)	None					780.2.h.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots\)
3120.2.l.m	$3120$	$2$	3120.l	5.b	$2$	$6$	$6$	$24.913$	6.0.5161984.1	None					1560.2.l.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(2-\beta _{4}-\beta _{5})q^{11}+\cdots\)
3120.2.l.n	$3120$	$2$	3120.l	5.b	$2$	$8$	$8$	$24.913$	8.0.\(\cdots\).2	None					1560.2.l.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{6}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
3120.2.l.o	$3120$	$2$	3120.l	5.b	$2$	$8$	$8$	$24.913$	8.0.1698758656.6	None					1560.2.l.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}+\beta _{4}q^{7}+\cdots\)
3120.2.l.p	$3120$	$2$	3120.l	5.b	$2$	$10$	$10$	$24.913$	10.0.\(\cdots\).1	None					195.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{9})q^{7}+\cdots\)
3120.2.l.q	$3120$	$2$	3120.l	5.b	$2$	$10$	$10$	$24.913$	10.0.\(\cdots\).1	None					1560.2.l.f	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{3}q^{5}-\beta _{9}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 2}\)