Space of modular forms of level 98, weight 2, and Character 98.e

• Label: 98.2.e
• Level: $98$
• Weight: $2$
• Character orbit: 98.e
• Rep. character: $\chi_{98}(15,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(98, [\chi])\).

	Total	New	Old
Modular forms	96	36	60
Cusp forms	72	36	36
Eisenstein series	24	0	24

Trace form

36 * q - 2 * q^3 - 6 * q^4 - 6 * q^5 + 8 * q^6 - 8 * q^7 - 6 * q^10 + 6 * q^11 - 2 * q^12 - 10 * q^13 - 6 * q^14 - 2 * q^15 - 6 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 + 8 * q^20 - 26 * q^21 + 6 * q^22 + 26 * q^23 - 6 * q^24 - 22 * q^25 - 4 * q^26 - 2 * q^27 - 8 * q^28 - 2 * q^29 - 16 * q^30 - 28 * q^31 - 48 * q^33 - 12 * q^34 - 28 * q^35 + 20 * q^37 - 4 * q^38 + 18 * q^39 + 8 * q^40 - 20 * q^41 + 96 * q^42 - 44 * q^43 + 6 * q^44 + 118 * q^45 + 26 * q^46 + 76 * q^47 + 12 * q^48 + 6 * q^49 - 24 * q^50 + 16 * q^51 + 18 * q^52 + 58 * q^53 + 6 * q^54 + 96 * q^55 + 8 * q^56 - 18 * q^57 + 60 * q^58 - 12 * q^59 - 2 * q^60 + 28 * q^61 - 22 * q^62 + 6 * q^63 - 6 * q^64 - 56 * q^65 - 48 * q^66 - 52 * q^67 + 4 * q^68 - 68 * q^69 - 28 * q^70 - 6 * q^71 - 8 * q^72 - 34 * q^73 - 10 * q^74 - 50 * q^75 - 22 * q^76 - 42 * q^77 + 24 * q^78 - 68 * q^79 + 8 * q^80 - 36 * q^81 - 36 * q^82 + 90 * q^83 + 16 * q^84 - 16 * q^85 + 18 * q^86 - 62 * q^87 + 6 * q^88 + 56 * q^89 - 36 * q^90 + 4 * q^91 - 16 * q^92 + 82 * q^93 + 10 * q^94 - 24 * q^95 - 6 * q^96 + 24 * q^97 - 20 * q^98 + 120 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.2.e.a	$98$	$2$	98.e	49.e	$7$	$18$	$3$	$0.783$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			98.2.e.a	$2$	$0$	\(-3\)	\(3\)	\(-6\)	\(-7\)	$7$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{13}q^{2}+(\beta _{1}-\beta _{14})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots\)
98.2.e.b	$98$	$2$	98.e	49.e	$7$	$18$	$3$	$0.783$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		✓			98.2.e.b	$2$	$0$	\(3\)	\(-5\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{9}q^{2}+\beta _{4}q^{3}+(-1-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(98, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)