Space of modular forms of level 140, weight 15, and Character 140.d

• Label: 140.15.d
• Level: $140$
• Weight: $15$
• Character orbit: 140.d
• Rep. character: $\chi_{140}(41,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $360$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	140.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(360\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(140, [\chi])\).

	Total	New	Old
Modular forms	342	36	306
Cusp forms	330	36	294
Eisenstein series	12	0	12

Trace form

\( 36 q + 1364266 q^{7} - 54790830 q^{9} + O(q^{10}) \)

Decomposition of \(S_{15}^{\mathrm{new}}(140, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
140.15.d.a	$140$	$15$	140.d	7.b	$2$	$36$	$36$	$174.061$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1364266\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{15}^{\mathrm{old}}(140, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(140, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)