Space of modular forms of level 1350, weight 3, and Character 1350.k

• Label: 1350.3.k
• Level: $1350$
• Weight: $3$
• Character orbit: 1350.k
• Rep. character: $\chi_{1350}(449,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $810$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1350.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(810\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1350, [\chi])\).

	Total	New	Old
Modular forms	1152	72	1080
Cusp forms	1008	72	936
Eisenstein series	144	0	144

Trace form

72 * q - 72 * q^4 + 72 * q^11 - 72 * q^14 - 144 * q^16 + 72 * q^29 + 60 * q^31 - 288 * q^41 + 48 * q^46 + 204 * q^49 + 144 * q^56 + 288 * q^59 - 96 * q^61 + 576 * q^64 + 288 * q^74 - 144 * q^79 + 216 * q^86 - 336 * q^91 + 168 * q^94

Decomposition of \(S_{3}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1350.3.k.a	$1350$	$3$	1350.k	45.h	$6$	$8$	$4$	$36.785$	\(\Q(\zeta_{24})\)	None					18.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{7}-\beta_{4})q^{2}-2\beta_{2} q^{4}+(3\beta_{7}+3\beta_{4}+\beta_1)q^{7}+\cdots\)
1350.3.k.b	$1350$	$3$	1350.k	45.h	$6$	$32$	$16$	$36.785$		None					90.3.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1350.3.k.c	$1350$	$3$	1350.k	45.h	$6$	$32$	$16$	$36.785$		None					450.3.i.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1350, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)