Space of modular forms of level 2592, weight 2, and Character 2592.d

• Label: 2592.2.d
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.d
• Rep. character: $\chi_{2592}(1297,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $11$
• Sturm bound: $864$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(864\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2592, [\chi])\).

	Total	New	Old
Modular forms	480	52	428
Cusp forms	384	44	340
Eisenstein series	96	8	88

Trace form

\( 44 q - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2592, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2592.2.d.a	$2592$	$2$	2592.d	8.b	$2$	$2$	$2$	$20.697$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}-4q^{7}-3iq^{11}+2iq^{13}+\cdots\)
2592.2.d.b	$2592$	$2$	2592.d	8.b	$2$	$2$	$2$	$20.697$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}-4q^{7}-3iq^{11}-2iq^{13}+\cdots\)
2592.2.d.c	$2592$	$2$	2592.d	8.b	$2$	$2$	$2$	$20.697$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+2q^{7}+\beta q^{13}-7q^{17}-2\beta q^{19}+\cdots\)
2592.2.d.d	$2592$	$2$	2592.d	8.b	$2$	$2$	$2$	$20.697$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}+2q^{7}-\beta q^{13}+7q^{17}+2\beta q^{19}+\cdots\)
2592.2.d.e	$2592$	$2$	2592.d	8.b	$2$	$4$	$4$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.d.f	$2592$	$2$	2592.d	8.b	$2$	$4$	$4$	$20.697$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2592.2.d.g	$2592$	$2$	2592.d	8.b	$2$	$4$	$4$	$20.697$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-1+\zeta_{12}^{3})q^{7}+\cdots\)
2592.2.d.h	$2592$	$2$	2592.d	8.b	$2$	$4$	$4$	$20.697$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\zeta_{12}+\zeta_{12}^{2})q^{5}+(-1+\zeta_{12}^{3})q^{7}+\cdots\)
2592.2.d.i	$2592$	$2$	2592.d	8.b	$2$	$4$	$4$	$20.697$	\(\Q(\sqrt{3}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+4q^{7}+2\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
2592.2.d.j	$2592$	$2$	2592.d	8.b	$2$	$8$	$8$	$20.697$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{6})q^{5}+(1-\beta _{5})q^{7}-\beta _{7}q^{11}+\cdots\)
2592.2.d.k	$2592$	$2$	2592.d	8.b	$2$	$8$	$8$	$20.697$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{6})q^{5}+(1-\beta _{5})q^{7}-\beta _{7}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2592, [\chi]) \cong \)