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

\( 76 q + O(q^{10}) \)

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

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

\( S_{2}^{\mathrm{old}}(7200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 12}\)