Space of modular forms of level 975, weight 2, and Character 975.w

• Label: 975.2.w
• Level: $975$
• Weight: $2$
• Character orbit: 975.w
• Rep. character: $\chi_{975}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $11$
• Sturm bound: $280$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(280\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

	Total	New	Old
Modular forms	304	80	224
Cusp forms	256	80	176
Eisenstein series	48	0	48

Trace form

80 * q - 36 * q^4 + 40 * q^9 + 24 * q^11 - 16 * q^14 - 20 * q^16 + 30 * q^19 - 32 * q^26 + 4 * q^29 + 36 * q^36 + 10 * q^39 - 24 * q^41 + 36 * q^46 - 42 * q^49 + 48 * q^51 + 76 * q^56 - 132 * q^59 + 24 * q^61 - 56 * q^64 + 28 * q^69 - 24 * q^71 - 32 * q^74 - 156 * q^76 + 64 * q^79 - 40 * q^81 - 24 * q^84 + 96 * q^89 - 86 * q^91 + 24 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
975.2.w.a	$975$	$2$	975.w	65.l	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None					195.2.bb.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
975.2.w.b	$975$	$2$	975.w	65.l	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		✓			975.2.bc.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
975.2.w.c	$975$	$2$	975.w	65.l	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		✓			975.2.bc.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
975.2.w.d	$975$	$2$	975.w	65.l	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None					39.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
975.2.w.e	$975$	$2$	975.w	65.l	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		✓			975.2.bc.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+(2\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots\)
975.2.w.f	$975$	$2$	975.w	65.l	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None					195.2.bb.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
975.2.w.g	$975$	$2$	975.w	65.l	$6$	$8$	$4$	$7.785$	8.0.56070144.2	None					195.2.bb.c	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{6}-\beta _{7})q^{2}-\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.h	$975$	$2$	975.w	65.l	$6$	$8$	$4$	$7.785$	8.0.191102976.5	None					195.2.bb.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5}+\beta _{7})q^{2}+\beta _{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.i	$975$	$2$	975.w	65.l	$6$	$8$	$4$	$7.785$	8.0.191102976.5	None					195.2.bb.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{5}+\beta _{7})q^{2}-\beta _{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.j	$975$	$2$	975.w	65.l	$6$	$8$	$4$	$7.785$	8.0.56070144.2	None					195.2.bb.c	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}-\beta _{6}+\beta _{7})q^{2}+\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.k	$975$	$2$	975.w	65.l	$6$	$24$	$12$	$7.785$		None		✓	✓		975.2.bc.k	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)