Space of modular forms of level 152, weight 2, and Character 152.q

• Label: 152.2.q
• Level: $152$
• Weight: $2$
• Character orbit: 152.q
• Rep. character: $\chi_{152}(9,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $30$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.q (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

	Total	New	Old
Modular forms	144	30	114
Cusp forms	96	30	66
Eisenstein series	48	0	48

Trace form

30 * q + 3 * q^3 - 9 * q^9 - 6 * q^13 + 12 * q^15 + 6 * q^17 - 6 * q^19 - 6 * q^21 + 12 * q^23 + 12 * q^25 - 27 * q^27 - 12 * q^29 - 6 * q^31 - 45 * q^33 - 18 * q^35 + 12 * q^37 - 36 * q^39 - 39 * q^41 - 48 * q^43 - 18 * q^45 - 21 * q^49 + 15 * q^51 - 18 * q^53 - 36 * q^55 + 36 * q^57 + 33 * q^59 - 6 * q^61 - 6 * q^63 + 42 * q^65 + 75 * q^67 + 24 * q^69 + 54 * q^71 + 54 * q^73 + 84 * q^75 + 36 * q^77 + 108 * q^79 + 69 * q^81 - 12 * q^85 + 54 * q^87 + 36 * q^89 + 84 * q^91 + 66 * q^93 - 78 * q^95 - 69 * q^97 - 3 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.2.q.a	$152$	$2$	152.q	19.e	$9$	$6$	$1$	$1.214$	\(\Q(\zeta_{18})\)	None		✓			152.2.q.a	$2$	$0$	\(0\)	\(-6\)	\(6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots\)
152.2.q.b	$152$	$2$	152.q	19.e	$9$	$6$	$1$	$1.214$	\(\Q(\zeta_{18})\)	None		✓			152.2.q.b	$2$	$0$	\(0\)	\(9\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots\)
152.2.q.c	$152$	$2$	152.q	19.e	$9$	$18$	$3$	$1.214$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓	✓		152.2.q.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(152, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)