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

• Label: 297.2.n
• Level: $297$
• Weight: $2$
• Character orbit: 297.n
• Rep. character: $\chi_{297}(37,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	336	112	224
Cusp forms	240	80	160
Eisenstein series	96	32	64

Trace form

80 * q + 5 * q^2 + 5 * q^4 + 2 * q^5 - 3 * q^7 + 8 * q^8 - 40 * q^10 + q^11 - 3 * q^13 + 11 * q^14 + 5 * q^16 + 8 * q^17 + 6 * q^19 + 21 * q^20 - 5 * q^22 - 6 * q^23 + 2 * q^25 + 28 * q^26 - 36 * q^28 + 32 * q^29 - 48 * q^32 + 2 * q^34 - 30 * q^35 - 18 * q^37 + 5 * q^38 - 13 * q^40 - 13 * q^41 - 2 * q^43 + 10 * q^44 + 11 * q^47 - 5 * q^49 + 24 * q^50 - 15 * q^52 - 32 * q^53 - 14 * q^55 - 102 * q^56 + 7 * q^58 + 13 * q^59 - 3 * q^61 - 190 * q^62 - 8 * q^64 - 52 * q^65 - 14 * q^67 + 32 * q^68 - 52 * q^70 + 6 * q^71 - 48 * q^73 - 81 * q^74 + 10 * q^76 + 37 * q^77 - 3 * q^79 + 4 * q^80 - 2 * q^82 + 10 * q^83 + 19 * q^85 + 56 * q^86 + 55 * q^88 + 128 * q^89 - 4 * q^91 - 29 * q^92 - 35 * q^94 + 81 * q^95 - 27 * q^97 + 256 * 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.n.a	$297$	$2$	297.n	99.m	$15$	$8$	$1$	$2.372$	\(\Q(\zeta_{15})\)	None					99.2.m.a	$4$	$0$	\(4\)	\(0\)	\(-6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}-\zeta_{15}^{6}+\cdots)q^{2}+\cdots\)
297.2.n.b	$297$	$2$	297.n	99.m	$15$	$72$	$9$	$2.372$		None			✓		99.2.m.b	$4$	$0$	\(1\)	\(0\)	\(8\)	\(-2\)		$\mathrm{SU}(2)[C_{15}]$

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

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