Space of modular forms of level 2700, weight 3, and Character 2700.u

• Label: 2700.3.u
• Level: $2700$
• Weight: $3$
• Character orbit: 2700.u
• Rep. character: $\chi_{2700}(449,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $1620$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2700.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1620\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2700, [\chi])\).

	Total	New	Old
Modular forms	2268	72	2196
Cusp forms	2052	72	1980
Eisenstein series	216	0	216

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2700, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2700.3.u.a	$2700$	$3$	2700.u	45.h	$6$	$8$	$4$	$73.570$	8.0.12960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(4\beta _{1}+\beta _{6})q^{7}+(-1+\beta _{2}+\beta _{5}+\beta _{7})q^{11}+\cdots\)
2700.3.u.b	$2700$	$3$	2700.u	45.h	$6$	$8$	$4$	$73.570$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{4}-2\beta _{7})q^{7}+(12-5\beta _{2}+\cdots)q^{11}+\cdots\)
2700.3.u.c	$2700$	$3$	2700.u	45.h	$6$	$24$	$12$	$73.570$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
2700.3.u.d	$2700$	$3$	2700.u	45.h	$6$	$32$	$16$	$73.570$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)