Space of modular forms of level 7200, weight 2, and Character 7200.b

• Label: 7200.2.b
• Level: $7200$
• Weight: $2$
• Character orbit: 7200.b
• Rep. character: $\chi_{7200}(4751,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $9$
• Sturm bound: $2880$
• Trace bound: $67$

Defining parameters

Level:	$N$	$=$	$7200 = 2^{5} \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	7200.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$24$
Character field:			$\Q$
Newform subspaces:			$9$
Sturm bound:			$2880$
Trace bound:			$67$
Distinguishing $T_p$:			$7$, $23$, $43$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(7200, [\chi])$.

	Total	New	Old
Modular forms	1536	76	1460
Cusp forms	1344	76	1268
Eisenstein series	192	0	192

Trace form

$76 q - 16 q^{19} + 32 q^{43} - 92 q^{49} + 16 q^{67} - 16 q^{73} - 48 q^{91}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(7200, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7200.2.b.a	$7200$	$2$	7200.b	24.f	$2$	$2$	$2$	$57.492$	$\Q(\sqrt{-2})$	None					360.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta q^{7}+\beta q^{11}-3\beta q^{13}-2\beta q^{17}+\cdots$
7200.2.b.b	$7200$	$2$	7200.b	24.f	$2$	$2$	$2$	$57.492$	$\Q(\sqrt{-2})$	None					360.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta q^{7}-\beta q^{11}-3\beta q^{13}+2\beta q^{17}+\cdots$
7200.2.b.c	$7200$	$2$	7200.b	24.f	$2$	$4$	$4$	$57.492$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					72.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{7}+2\beta _{1}q^{11}+\beta _{3}q^{13}-\beta _{1}q^{17}+\cdots$
7200.2.b.d	$7200$	$2$	7200.b	24.f	$2$	$6$	$6$	$57.492$	6.0.2580992.1	None					360.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(\beta _{1}-\beta _{3}+\cdots)q^{13}+\cdots$
7200.2.b.e	$7200$	$2$	7200.b	24.f	$2$	$6$	$6$	$57.492$	6.0.2580992.1	None					360.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{7}+(\beta _{1}+\beta _{3})q^{11}+(\beta _{1}-\beta _{3}+\cdots)q^{13}+\cdots$
7200.2.b.f	$7200$	$2$	7200.b	24.f	$2$	$8$	$8$	$57.492$	8.0.40960000.1	$\Q(\sqrt{-10})$					360.2.m.a	$8$	$0$	$0$	$0$	$0$	$0$	$2^{11}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{7}+\beta _{2}q^{11}+\beta _{3}q^{13}+\beta _{7}q^{19}+\cdots$
7200.2.b.g	$7200$	$2$	7200.b	24.f	$2$	$16$	$16$	$57.492$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					1800.2.b.h	$4$	$0$	$0$	$0$	$0$	$0$	$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{13}q^{7}+\beta _{15}q^{11}-\beta _{10}q^{13}+(\beta _{6}+\cdots)q^{17}+\cdots$
7200.2.b.h	$7200$	$2$	7200.b	24.f	$2$	$16$	$16$	$57.492$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					1800.2.b.h	$4$	$0$	$0$	$0$	$0$	$0$	$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{13}q^{7}-\beta _{15}q^{11}-\beta _{10}q^{13}+(\beta _{6}+\cdots)q^{17}+\cdots$
7200.2.b.i	$7200$	$2$	7200.b	24.f	$2$	$16$	$16$	$57.492$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					360.2.m.c	$8$	$0$	$0$	$0$	$0$	$0$	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{7}+(-\beta _{7}-\beta _{8})q^{11}+\beta _{6}q^{13}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(7200, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(7200, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(24, [\chi])$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(72, [\chi])$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(96, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(120, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(288, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(360, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(480, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(600, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(1440, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1800, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(2400, [\chi])$$^{\oplus 2}$