Space of modular forms of level 5400, weight 2, and Character 5400.f

• Label: 5400.2.f
• Level: $5400$
• Weight: $2$
• Character orbit: 5400.f
• Rep. character: $\chi_{5400}(649,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $32$
• Sturm bound: $2160$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 5400 = 2^{3} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5400.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 32 \)
Sturm bound:			\(2160\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5400, [\chi])\).

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

Trace form

\( 72 q + 4 q^{31} - 84 q^{49} - 48 q^{61} - 52 q^{79} - 68 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5400, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5400.2.f.a	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.s	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}-6 q^{11}-6 i q^{13}-2 i q^{17}+\cdots\)
5400.2.f.b	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					216.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{7}-5 q^{11}-4 i q^{13}+8 i q^{17}+\cdots\)
5400.2.f.c	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-5 q^{11}-i q^{13}+2 i q^{17}+\cdots\)
5400.2.f.d	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{7}-4 q^{11}+6 i q^{13}+6 i q^{17}+\cdots\)
5400.2.f.e	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					216.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{7}-4 q^{11}+i q^{13}-4 i q^{17}+\cdots\)
5400.2.f.f	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-4 q^{11}+2 i q^{13}-5 i q^{17}+\cdots\)
5400.2.f.g	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}-4 q^{11}+i q^{13}+8 i q^{17}+\cdots\)
5400.2.f.h	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-3 q^{11}-3 i q^{13}-2 i q^{17}+\cdots\)
5400.2.f.i	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.t	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}-2 q^{11}-2 i q^{13}-2 i q^{17}+\cdots\)
5400.2.f.j	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{11}-3 i q^{17}+q^{19}+3 i q^{23}+\cdots\)
5400.2.f.k	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}-2 q^{11}-5 i q^{13}+4 i q^{17}+\cdots\)
5400.2.f.l	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}-2 q^{11}+4 i q^{13}+i q^{17}+\cdots\)
5400.2.f.m	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-q^{11}-i q^{13}+i q^{17}+\cdots\)
5400.2.f.n	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-6 i q^{13}-7 i q^{17}-7 q^{19}+\cdots\)
5400.2.f.o	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-6 i q^{13}+7 i q^{17}-7 q^{19}+\cdots\)
5400.2.f.p	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}+q^{11}-i q^{13}-i q^{17}+\cdots\)
5400.2.f.q	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.t	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}+2 q^{11}-2 i q^{13}+2 i q^{17}+\cdots\)
5400.2.f.r	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{11}-3 i q^{17}+q^{19}+3 i q^{23}+\cdots\)
5400.2.f.s	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}+2 q^{11}+4 i q^{13}-i q^{17}+\cdots\)
5400.2.f.t	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}+2 q^{11}-5 i q^{13}-4 i q^{17}+\cdots\)
5400.2.f.u	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}+3 q^{11}-3 i q^{13}+2 i q^{17}+\cdots\)
5400.2.f.v	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					216.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{7}+4 q^{11}+i q^{13}+4 i q^{17}+\cdots\)
5400.2.f.w	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{7}+4 q^{11}+6 i q^{13}-6 i q^{17}+\cdots\)
5400.2.f.x	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					1080.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}+4 q^{11}+2 i q^{13}+5 i q^{17}+\cdots\)
5400.2.f.y	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}+4 q^{11}+i q^{13}-8 i q^{17}+\cdots\)
5400.2.f.z	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None					216.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{7}+5 q^{11}-4 i q^{13}-8 i q^{17}+\cdots\)
5400.2.f.ba	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}+5 q^{11}-i q^{13}-2 i q^{17}+\cdots\)
5400.2.f.bb	$5400$	$2$	5400.f	5.b	$2$	$2$	$2$	$43.119$	\(\Q(\sqrt{-1}) \)	None		✓			5400.2.a.s	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}+6 q^{11}-6 i q^{13}+2 i q^{17}+\cdots\)
5400.2.f.bc	$5400$	$2$	5400.f	5.b	$2$	$4$	$4$	$43.119$	\(\Q(i, \sqrt{13})\)	None		✓			5400.2.a.bx	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{7}-q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
5400.2.f.bd	$5400$	$2$	5400.f	5.b	$2$	$4$	$4$	$43.119$	\(\Q(i, \sqrt{73})\)	None					1080.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{7}-\beta _{3}q^{11}+3\beta _{2}q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
5400.2.f.be	$5400$	$2$	5400.f	5.b	$2$	$4$	$4$	$43.119$	\(\Q(i, \sqrt{73})\)	None					1080.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{7}+\beta _{3}q^{11}+3\beta _{2}q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
5400.2.f.bf	$5400$	$2$	5400.f	5.b	$2$	$4$	$4$	$43.119$	\(\Q(i, \sqrt{13})\)	None		✓			5400.2.a.bx	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{7}+q^{11}+(2\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2700, [\chi])\)\(^{\oplus 2}\)