Space of modular forms of level 64, weight 7, and Character 64.c

• Label: 64.7.c
• Level: $64$
• Weight: $7$
• Character orbit: 64.c
• Rep. character: $\chi_{64}(63,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $56$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	64.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(56\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(64, [\chi])\).

	Total	New	Old
Modular forms	54	13	41
Cusp forms	42	11	31
Eisenstein series	12	2	10

Trace form

11 * q + 2 * q^5 - 2189 * q^9 + 5042 * q^13 + 4886 * q^17 + 17984 * q^21 + 32169 * q^25 - 33198 * q^29 + 45536 * q^33 - 51838 * q^37 - 75162 * q^41 + 287602 * q^45 - 84037 * q^49 - 79262 * q^53 - 242784 * q^57 - 523054 * q^61 - 131796 * q^65 - 255808 * q^69 + 162502 * q^73 + 93632 * q^77 + 1372859 * q^81 - 1142012 * q^85 - 1101850 * q^89 + 3193088 * q^93 + 1393462 * q^97

Decomposition of \(S_{7}^{\mathrm{new}}(64, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.7.c.a	$64$	$7$	64.c	4.b	$2$	$1$	$1$	$14.723$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				16.7.c.a	$2$	$0$	\(0\)	\(0\)	\(-234\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-234q^{5}+3^{6}q^{9}+4070q^{13}-990q^{17}+\cdots\)
64.7.c.b	$64$	$7$	64.c	4.b	$2$	$2$	$2$	$14.723$	\(\Q(\sqrt{-1}) \)	None					32.7.c.a	$2$	$0$	\(0\)	\(0\)	\(-100\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-50 q^{5}-46\beta q^{7}+713 q^{9}+\cdots\)
64.7.c.c	$64$	$7$	64.c	4.b	$2$	$2$	$2$	$14.723$	\(\Q(\sqrt{-15}) \)	None					4.7.b.a	$2$	$0$	\(0\)	\(0\)	\(-20\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-10q^{5}-10\beta q^{7}-231q^{9}+\cdots\)
64.7.c.d	$64$	$7$	64.c	4.b	$2$	$2$	$2$	$14.723$	\(\Q(\sqrt{-3}) \)	None					16.7.c.b	$2$	$0$	\(0\)	\(0\)	\(300\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+150 q^{5}+22\beta q^{7}-39 q^{9}+\cdots\)
64.7.c.e	$64$	$7$	64.c	4.b	$2$	$4$	$4$	$14.723$	\(\Q(i, \sqrt{6})\)	None			✓		32.7.c.b	$2$	$0$	\(0\)	\(0\)	\(56\)	\(0\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(14+\beta _{3})q^{5}+(-2\beta _{1}+5\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(64, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(64, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)