Space of modular forms of level 297, weight 2, and Character 297.e

• Label: 297.2.e
• Level: $297$
• Weight: $2$
• Character orbit: 297.e
• Rep. character: $\chi_{297}(100,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $72$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(72\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(297, [\chi])\).

	Total	New	Old
Modular forms	84	20	64
Cusp forms	60	20	40
Eisenstein series	24	0	24

Trace form

20 * q - 10 * q^4 + 3 * q^5 - 2 * q^7 + 12 * q^8 + 4 * q^11 - 2 * q^13 - 6 * q^14 - 10 * q^16 + 12 * q^17 + 4 * q^19 - 6 * q^20 + 6 * q^23 - 7 * q^25 - 48 * q^26 + 16 * q^28 - 12 * q^29 - 5 * q^31 - 12 * q^32 - 12 * q^34 - 2 * q^37 + 30 * q^38 - 12 * q^40 - 12 * q^41 - 8 * q^43 - 20 * q^44 - 6 * q^47 + 6 * q^50 + 10 * q^52 + 12 * q^53 - 6 * q^55 + 12 * q^56 + 18 * q^58 + 27 * q^59 - 2 * q^61 + 60 * q^62 + 8 * q^64 - 18 * q^65 - 11 * q^67 + 18 * q^68 + 12 * q^70 - 66 * q^71 + 28 * q^73 - 54 * q^74 - 20 * q^76 + 8 * q^77 - 2 * q^79 + 96 * q^80 + 12 * q^82 - 24 * q^85 - 36 * q^86 + 12 * q^89 + 44 * q^91 + 54 * q^92 + 30 * q^94 - 36 * q^95 - 23 * q^97 - 36 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(297, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
297.2.e.a	$297$	$2$	297.e	9.c	$3$	$2$	$1$	$2.372$	\(\Q(\sqrt{-3}) \)	None					99.2.e.c	$2$	$1$	\(-2\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
297.2.e.b	$297$	$2$	297.e	9.c	$3$	$2$	$1$	$2.372$	\(\Q(\sqrt{-3}) \)	None					99.2.e.b	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
297.2.e.c	$297$	$2$	297.e	9.c	$3$	$2$	$1$	$2.372$	\(\Q(\sqrt{-3}) \)	None					99.2.e.a	$2$	$0$	\(1\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
297.2.e.d	$297$	$2$	297.e	9.c	$3$	$6$	$3$	$2.372$	\(\Q(\zeta_{18})\)	None					99.2.e.d	$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots\)
297.2.e.e	$297$	$2$	297.e	9.c	$3$	$8$	$4$	$2.372$	8.0.508277025.1	None			✓		99.2.e.e	$2$	$0$	\(1\)	\(0\)	\(4\)	\(-1\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{3}+3\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(297, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(297, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)