Space of modular forms of level 10, weight 19, and Character 10.c

• Label: 10.19.c
• Level: $10$
• Weight: $19$
• Character orbit: 10.c
• Rep. character: $\chi_{10}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
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:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(10, [\chi])\).

	Total	New	Old
Modular forms	58	18	40
Cusp forms	50	18	32
Eisenstein series	8	0	8

Trace form

\( 18 q - 512 q^{2} + 40256 q^{3} - 4568580 q^{5} + 17303552 q^{6} - 115408296 q^{7} + 67108864 q^{8} + O(q^{10}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(10, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.19.c.a	$10$	$19$	10.c	5.c	$4$	$8$	$4$	$20.539$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(2048\)	\(37026\)	\(-3132450\)	\(-43579766\)	$2^{15}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{8}-2^{8}\beta _{1})q^{2}+(4628+4628\beta _{1}+\cdots)q^{3}+\cdots\)
10.19.c.b	$10$	$19$	10.c	5.c	$4$	$10$	$5$	$20.539$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(-2560\)	\(3230\)	\(-1436130\)	\(-71828530\)	$2^{22}\cdot 3^{8}\cdot 5^{17}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2^{8}-2^{8}\beta _{1})q^{2}+(323-323\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{19}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{19}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{19}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)