Space of modular forms of level 108, weight 3, and Character 108.f

• Label: 108.3.f
• Level: $108$
• Weight: $3$
• Character orbit: 108.f
• Rep. character: $\chi_{108}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $54$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$108 = 2^{2} \cdot 3^{3}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	108.f (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$36$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$3$
Sturm bound:			$54$
Trace bound:			$2$
Distinguishing $T_p$:			$5$, $7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(108, [\chi])$.

	Total	New	Old
Modular forms	84	28	56
Cusp forms	60	20	40
Eisenstein series	24	8	16

Trace form

20 * q + q^2 - q^4 + 2 * q^5 + 22 * q^8 + 4 * q^10 - 2 * q^13 + 24 * q^14 - q^16 + 32 * q^17 - 52 * q^20 - 9 * q^22 - 12 * q^25 - 160 * q^26 - 36 * q^28 + 26 * q^29 - 119 * q^32 - 11 * q^34 - 8 * q^37 + 153 * q^38 + 4 * q^40 - 58 * q^41 + 390 * q^44 - 96 * q^46 - 16 * q^49 + 237 * q^50 + 22 * q^52 - 136 * q^53 - 270 * q^56 + 52 * q^58 - 2 * q^61 - 564 * q^62 + 2 * q^64 - 146 * q^65 - 331 * q^68 + 102 * q^70 + 16 * q^73 + 404 * q^74 + 93 * q^76 + 246 * q^77 + 848 * q^80 + 202 * q^82 - 52 * q^85 + 447 * q^86 + 75 * q^88 + 392 * q^89 - 426 * q^92 + 48 * q^94 - 62 * q^97 - 1022 * q^98

Decomposition of $S_{3}^{\mathrm{new}}(108, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.3.f.a	$108$	$3$	108.f	36.f	$6$	$2$	$1$	$2.943$	$\Q(\sqrt{-3})$	None					36.3.f.a	$2$	$0$	$-4$	$0$	$4$	$-6$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2q^{2}+4q^{4}+(4-4\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots$
108.3.f.b	$108$	$3$	108.f	36.f	$6$	$2$	$1$	$2.943$	$\Q(\sqrt{-3})$	None					36.3.f.a	$2$	$0$	$2$	$0$	$4$	$6$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots$
108.3.f.c	$108$	$3$	108.f	36.f	$6$	$16$	$8$	$2.943$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None			✓		36.3.f.c	$4$	$0$	$3$	$0$	$-6$	$0$	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$

Decomposition of $S_{3}^{\mathrm{old}}(108, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(108, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(36, [\chi])$$^{\oplus 2}$