Space of modular forms of level 325, weight 3, and Character 325.w

• Label: 325.3.w
• Level: $325$
• Weight: $3$
• Character orbit: 325.w
• Rep. character: $\chi_{325}(24,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $160$
• Newform subspaces: $6$
• Sturm bound: $105$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(105\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(325, [\chi])\).

	Total	New	Old
Modular forms	304	176	128
Cusp forms	256	160	96
Eisenstein series	48	16	32

Trace form

160 * q + 12 * q^4 + 8 * q^6 + 220 * q^9 - 16 * q^11 - 16 * q^14 + 348 * q^16 + 60 * q^19 - 40 * q^21 + 68 * q^24 - 124 * q^26 + 76 * q^29 + 80 * q^31 - 176 * q^34 - 96 * q^36 - 64 * q^39 + 340 * q^41 + 40 * q^44 + 728 * q^46 + 144 * q^49 - 712 * q^54 - 1320 * q^56 - 8 * q^59 - 216 * q^61 - 680 * q^66 + 432 * q^69 + 824 * q^71 + 504 * q^74 - 212 * q^76 + 112 * q^79 + 80 * q^81 - 136 * q^84 - 336 * q^86 + 1240 * q^89 - 1212 * q^91 - 188 * q^94 - 300 * q^96 - 1576 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(325, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
325.3.w.a	$325$	$3$	325.w	65.s	$12$	$4$	$1$	$8.856$	\(\Q(\zeta_{12})\)	None					13.3.f.a	$2$	$0$	\(-4\)	\(-6\)	\(0\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12})q^{2}+(-2+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
325.3.w.b	$325$	$3$	325.w	65.s	$12$	$4$	$1$	$8.856$	\(\Q(\zeta_{12})\)	None					13.3.f.a	$2$	$0$	\(4\)	\(6\)	\(0\)	\(20\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12})q^{2}+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
325.3.w.c	$325$	$3$	325.w	65.s	$12$	$36$	$9$	$8.856$		None		✓			325.3.t.b	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$
325.3.w.d	$325$	$3$	325.w	65.s	$12$	$36$	$9$	$8.856$		None		✓			325.3.t.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$
325.3.w.e	$325$	$3$	325.w	65.s	$12$	$40$	$10$	$8.856$		None					65.3.p.a	$2$	$0$	\(0\)	\(-12\)	\(0\)	\(-44\)		$\mathrm{SU}(2)[C_{12}]$
325.3.w.f	$325$	$3$	325.w	65.s	$12$	$40$	$10$	$8.856$		None					65.3.p.a	$2$	$0$	\(0\)	\(12\)	\(0\)	\(44\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{3}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)