Space of modular forms of level 4368, weight 2, and Character 4368.h

• Label: 4368.2.h
• Level: $4368$
• Weight: $2$
• Character orbit: 4368.h
• Rep. character: $\chi_{4368}(337,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $20$
• Sturm bound: $1792$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4368.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1792\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4368, [\chi])\).

	Total	New	Old
Modular forms	920	84	836
Cusp forms	872	84	788
Eisenstein series	48	0	48

Trace form

\( 84 q + 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4368, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4368.2.h.a	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+4iq^{5}-iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots\)
4368.2.h.b	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+3iq^{5}+iq^{7}+q^{9}-5iq^{11}+\cdots\)
4368.2.h.c	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+iq^{7}+q^{9}+4iq^{11}+(-3+\cdots)q^{13}+\cdots\)
4368.2.h.d	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+iq^{5}+iq^{7}+q^{9}+(2+3i)q^{13}+\cdots\)
4368.2.h.e	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+3iq^{5}+iq^{7}+q^{9}+(2-3i)q^{13}+\cdots\)
4368.2.h.f	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2iq^{5}-iq^{7}+q^{9}+(2+3i)q^{13}+\cdots\)
4368.2.h.g	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+3iq^{5}-iq^{7}+q^{9}+4iq^{11}+\cdots\)
4368.2.h.h	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+iq^{5}-iq^{7}+q^{9}+3iq^{11}+\cdots\)
4368.2.h.i	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+3iq^{5}-iq^{7}+q^{9}-5iq^{11}+\cdots\)
4368.2.h.j	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
4368.2.h.k	$4368$	$2$	4368.h	13.b	$2$	$2$	$2$	$34.879$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
4368.2.h.l	$4368$	$2$	4368.h	13.b	$2$	$4$	$4$	$34.879$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
4368.2.h.m	$4368$	$2$	4368.h	13.b	$2$	$4$	$4$	$34.879$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{2}q^{5}-\beta _{2}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
4368.2.h.n	$4368$	$2$	4368.h	13.b	$2$	$4$	$4$	$34.879$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
4368.2.h.o	$4368$	$2$	4368.h	13.b	$2$	$6$	$6$	$34.879$	6.0.350464.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{5}+\beta _{4}q^{7}+\cdots\)
4368.2.h.p	$4368$	$2$	4368.h	13.b	$2$	$6$	$6$	$34.879$	6.0.350464.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
4368.2.h.q	$4368$	$2$	4368.h	13.b	$2$	$8$	$8$	$34.879$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta _{2}-\beta _{7})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
4368.2.h.r	$4368$	$2$	4368.h	13.b	$2$	$10$	$10$	$34.879$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+q^{9}+(\beta _{3}-\beta _{9})q^{11}+\cdots\)
4368.2.h.s	$4368$	$2$	4368.h	13.b	$2$	$10$	$10$	$34.879$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-\beta _{1}-\beta _{6})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
4368.2.h.t	$4368$	$2$	4368.h	13.b	$2$	$10$	$10$	$34.879$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(\beta _{1}+\beta _{5})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1456, [\chi])\)\(^{\oplus 2}\)