Space of modular forms of level 4140, weight 2, and Character 4140.f

• Label: 4140.2.f
• Level: $4140$
• Weight: $2$
• Character orbit: 4140.f
• Rep. character: $\chi_{4140}(829,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $1728$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4140.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1728\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4140, [\chi])\).

	Total	New	Old
Modular forms	888	56	832
Cusp forms	840	56	784
Eisenstein series	48	0	48

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4140, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4140.2.f.a	$4140$	$2$	4140.f	5.b	$2$	$6$	$6$	$33.058$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{4})q^{5}-\beta _{3}q^{7}+\beta _{1}q^{11}+(\beta _{3}+\cdots)q^{13}+\cdots\)
4140.2.f.b	$4140$	$2$	4140.f	5.b	$2$	$12$	$12$	$33.058$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{5}+(\beta _{1}+\beta _{6}-\beta _{10})q^{7}+(-1+\cdots)q^{11}+\cdots\)
4140.2.f.c	$4140$	$2$	4140.f	5.b	$2$	$14$	$14$	$33.058$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{5}+\beta _{13}q^{7}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
4140.2.f.d	$4140$	$2$	4140.f	5.b	$2$	$24$	$24$	$33.058$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)