Space of modular forms of level 912, weight 2, and Character 912.bo

• Label: 912.2.bo
• Level: $912$
• Weight: $2$
• Character orbit: 912.bo
• Rep. character: $\chi_{912}(289,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $120$
• Newform subspaces: $12$
• Sturm bound: $320$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(320\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

	Total	New	Old
Modular forms	1032	120	912
Cusp forms	888	120	768
Eisenstein series	144	0	144

Trace form

\( 120 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.2.bo.a	$912$	$2$	912.bo	19.e	$9$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-9\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}-\zeta_{18}^{3}-2\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.b	$912$	$2$	912.bo	19.e	$9$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.c	$912$	$2$	912.bo	19.e	$9$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{3}+(-1+\zeta_{18}^{2}+\zeta_{18}^{3}-2\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
912.2.bo.d	$912$	$2$	912.bo	19.e	$9$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{3}+(1-\zeta_{18}^{2}-\zeta_{18}^{3}-2\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
912.2.bo.e	$912$	$2$	912.bo	19.e	$9$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\zeta_{18}q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.f	$912$	$2$	912.bo	19.e	$9$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	None		$2$	$0$	\(0\)	\(0\)	\(9\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\zeta_{18}q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+2\zeta_{18}^{5})q^{5}+\cdots\)
912.2.bo.g	$912$	$2$	912.bo	19.e	$9$	$12$	$2$	$7.282$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{5}+\beta _{8}+\beta _{9}+\cdots)q^{5}+\cdots\)
912.2.bo.h	$912$	$2$	912.bo	19.e	$9$	$12$	$2$	$7.282$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}+\beta _{11})q^{3}-\beta _{1}q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.bo.i	$912$	$2$	912.bo	19.e	$9$	$12$	$2$	$7.282$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{3}q^{3}+(\beta _{3}-\beta _{5}+\beta _{10})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.bo.j	$912$	$2$	912.bo	19.e	$9$	$12$	$2$	$7.282$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(9\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{3}q^{3}+(1-2\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
912.2.bo.k	$912$	$2$	912.bo	19.e	$9$	$18$	$3$	$7.282$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+\beta _{7}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
912.2.bo.l	$912$	$2$	912.bo	19.e	$9$	$18$	$3$	$7.282$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q-\beta _{9}q^{3}+(1+\beta _{5}-\beta _{6}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)