Space of modular forms of level 540, weight 3, and Character 540.b

• Label: 540.3.b
• Level: $540$
• Weight: $3$
• Character orbit: 540.b
• Rep. character: $\chi_{540}(269,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $324$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	540.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(324\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(540, [\chi])\).

	Total	New	Old
Modular forms	234	16	218
Cusp forms	198	16	182
Eisenstein series	36	0	36

Trace form

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(540, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
540.3.b.a	$540$	$3$	540.b	15.d	$2$	$4$	$4$	$14.714$	\(\Q(\sqrt{-11}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{11}+\cdots\)
540.3.b.b	$540$	$3$	540.b	15.d	$2$	$4$	$4$	$14.714$	\(\Q(\sqrt{-11}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{5}-\beta _{2}q^{7}+(2\beta _{1}+3\beta _{2}+\cdots)q^{11}+\cdots\)
540.3.b.c	$540$	$3$	540.b	15.d	$2$	$8$	$8$	$14.714$	8.0.\(\cdots\).13	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-\beta _{6}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)