Space of modular forms of level 1920, weight 2, and Character 1920.f

• Label: 1920.2.f
• Level: $1920$
• Weight: $2$
• Character orbit: 1920.f
• Rep. character: $\chi_{1920}(769,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $16$
• Sturm bound: $768$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(768\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(11\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1920, [\chi])\).

	Total	New	Old
Modular forms	416	48	368
Cusp forms	352	48	304
Eisenstein series	64	0	64

Trace form

\( 48 q - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1920, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1920.2.f.a	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-2+i)q^{5}-q^{9}-4q^{11}+\cdots\)
1920.2.f.b	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.b	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-2-i)q^{5}+4iq^{7}-q^{9}+\cdots\)
1920.2.f.c	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.b	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-2+i)q^{5}+4iq^{7}-q^{9}+\cdots\)
1920.2.f.d	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-2-i)q^{5}-q^{9}+4q^{11}+\cdots\)
1920.2.f.e	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.e	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1+2i)q^{5}-q^{9}-2q^{11}+\cdots\)
1920.2.f.f	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.e	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(-1+2i)q^{5}-q^{9}+2q^{11}+\cdots\)
1920.2.f.g	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.e	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(1+2i)q^{5}-q^{9}-2q^{11}+\cdots\)
1920.2.f.h	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.e	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(1+2i)q^{5}-q^{9}+2q^{11}+\cdots\)
1920.2.f.i	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(2-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
1920.2.f.j	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(2+i)q^{5}+4iq^{7}-q^{9}+6iq^{13}+\cdots\)
1920.2.f.k	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(2-i)q^{5}+4iq^{7}-q^{9}-6iq^{13}+\cdots\)
1920.2.f.l	$1920$	$2$	1920.f	5.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		✓	1920.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+(2+i)q^{5}-q^{9}+4q^{11}-2iq^{13}+\cdots\)
1920.2.f.m	$1920$	$2$	1920.f	5.b	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓	1920.2.f.m	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
1920.2.f.n	$1920$	$2$	1920.f	5.b	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓	1920.2.f.m	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
1920.2.f.o	$1920$	$2$	1920.f	5.b	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓	1920.2.f.m	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
1920.2.f.p	$1920$	$2$	1920.f	5.b	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓	1920.2.f.m	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(2\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)