Space of modular forms of level 10, weight 17, and Character 10.c

• Label: 10.17.c
• Level: $10$
• Weight: $17$
• Character orbit: 10.c
• Rep. character: $\chi_{10}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $25$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(25\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(10, [\chi])\).

	Total	New	Old
Modular forms	52	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

\( 16 q - 15820 q^{3} - 31620 q^{5} - 1294336 q^{6} + 1540580 q^{7} + O(q^{10}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(10, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.17.c.a	$10$	$17$	10.c	5.c	$4$	$8$	$4$	$16.232$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-1024\)	\(-5382\)	\(184830\)	\(-1586702\)	$2^{13}\cdot 3^{8}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{7}+2^{7}\beta _{1})q^{2}+(-673-673\beta _{1}+\cdots)q^{3}+\cdots\)
10.17.c.b	$10$	$17$	10.c	5.c	$4$	$8$	$4$	$16.232$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(1024\)	\(-10438\)	\(-216450\)	\(3127282\)	$2^{13}\cdot 3^{2}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{7}+2^{7}\beta _{1})q^{2}+(-1305+1305\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{17}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{17}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{17}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)