Space of modular forms of level 190, weight 2, and Character 190.k

• Label: 190.2.k
• Level: $190$
• Weight: $2$
• Character orbit: 190.k
• Rep. character: $\chi_{190}(61,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $60$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.k (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(60\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(190, [\chi])\).

	Total	New	Old
Modular forms	204	48	156
Cusp forms	156	48	108
Eisenstein series	48	0	48

Trace form

48 * q + 6 * q^3 + 6 * q^6 + 6 * q^8 + 6 * q^9 - 24 * q^13 - 12 * q^14 - 12 * q^17 - 36 * q^18 + 12 * q^19 - 24 * q^22 - 24 * q^23 + 6 * q^24 - 6 * q^26 - 6 * q^27 + 12 * q^28 + 12 * q^29 - 12 * q^31 + 42 * q^33 + 24 * q^34 + 6 * q^35 + 6 * q^36 + 24 * q^37 + 18 * q^38 - 24 * q^39 - 12 * q^41 + 24 * q^42 + 36 * q^43 - 6 * q^44 - 84 * q^47 - 12 * q^48 - 60 * q^49 + 6 * q^50 + 18 * q^51 + 12 * q^52 - 84 * q^53 - 54 * q^54 + 24 * q^56 - 84 * q^57 - 48 * q^58 - 78 * q^59 + 60 * q^61 - 60 * q^62 - 60 * q^63 - 24 * q^64 + 18 * q^65 + 30 * q^66 + 18 * q^67 - 6 * q^68 - 36 * q^69 + 36 * q^71 - 12 * q^72 + 24 * q^73 + 18 * q^74 + 6 * q^76 + 72 * q^77 + 36 * q^78 + 72 * q^79 - 6 * q^81 + 42 * q^82 + 36 * q^83 + 84 * q^87 + 12 * q^88 + 84 * q^89 + 24 * q^90 + 12 * q^91 + 12 * q^92 + 72 * q^93 + 60 * q^94 + 18 * q^97 + 24 * q^98 + 144 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(190, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
190.2.k.a	$190$	$2$	190.k	19.e	$9$	$6$	$1$	$1.517$	\(\Q(\zeta_{18})\)	None		✓			190.2.k.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
190.2.k.b	$190$	$2$	190.k	19.e	$9$	$12$	$2$	$1.517$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			190.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
190.2.k.c	$190$	$2$	190.k	19.e	$9$	$12$	$2$	$1.517$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			190.2.k.c	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{8}q^{2}+(1+\beta _{4}+\beta _{7}+\beta _{10}-\beta _{11})q^{3}+\cdots\)
190.2.k.d	$190$	$2$	190.k	19.e	$9$	$18$	$3$	$1.517$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓	✓		190.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{9}q^{2}-\beta _{7}q^{3}-\beta _{11}q^{4}+\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(190, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(190, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)