Space of modular forms of level 119, weight 5, and Character 119.d

• Label: 119.5.d
• Level: $119$
• Weight: $5$
• Character orbit: 119.d
• Rep. character: $\chi_{119}(118,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 119 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(119, [\chi])\).

	Total	New	Old
Modular forms	50	50	0
Cusp forms	46	46	0
Eisenstein series	4	4	0

Trace form

46 * q - 4 * q^2 + 348 * q^4 - 68 * q^8 + 1062 * q^9 - 776 * q^15 + 1388 * q^16 - 2004 * q^18 - 504 * q^21 + 4774 * q^25 + 7970 * q^30 + 1398 * q^32 - 3184 * q^35 + 6534 * q^36 - 10822 * q^42 + 608 * q^43 - 2922 * q^49 - 6234 * q^50 - 4608 * q^51 + 10352 * q^53 - 23326 * q^60 + 7372 * q^64 + 6688 * q^67 + 11792 * q^70 - 53626 * q^72 + 6720 * q^77 + 23750 * q^81 + 32784 * q^84 - 20968 * q^85 - 75518 * q^86 + 8448 * q^93 - 15340 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(119, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
119.5.d.a	$119$	$5$	119.d	119.d	$2$	$5$	$5$	$12.301$	5.5.44253125.1	\(\Q(\sqrt{-119}) \)	✓	✓			119.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(245\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{4})q^{2}+(-6\beta _{1}-\beta _{4})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
119.5.d.b	$119$	$5$	119.d	119.d	$2$	$5$	$5$	$12.301$	5.5.44253125.1	\(\Q(\sqrt{-119}) \)	✓	✓			119.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-245\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{4})q^{2}+(6\beta _{1}+\beta _{4})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
119.5.d.c	$119$	$5$	119.d	119.d	$2$	$36$	$36$	$12.301$		None		✓	✓		119.5.d.c	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$