Space of modular forms of level 930, weight 2, and Character 930.j

• Label: 930.2.j
• Level: $930$
• Weight: $2$
• Character orbit: 930.j
• Rep. character: $\chi_{930}(497,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $120$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

	Total	New	Old
Modular forms	400	120	280
Cusp forms	368	120	248
Eisenstein series	32	0	32

Trace form

120 * q + 8 * q^6 - 24 * q^15 - 120 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 40 * q^33 + 8 * q^36 + 16 * q^37 - 16 * q^40 - 32 * q^42 - 48 * q^43 + 56 * q^45 - 48 * q^46 + 32 * q^51 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 16 * q^60 + 80 * q^61 - 48 * q^63 - 48 * q^66 - 16 * q^67 - 32 * q^70 + 16 * q^72 + 80 * q^73 - 64 * q^75 + 16 * q^78 + 40 * q^81 + 32 * q^82 - 80 * q^85 + 40 * q^87 - 32 * q^90 - 8 * q^96 - 32 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
930.2.j.a	$930$	$2$	930.j	15.e	$4$	$4$	$2$	$7.426$	\(\Q(\zeta_{8})\)	None		✓			930.2.j.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
930.2.j.b	$930$	$2$	930.j	15.e	$4$	$4$	$2$	$7.426$	\(\Q(\zeta_{8})\)	None		✓			930.2.j.b	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
930.2.j.c	$930$	$2$	930.j	15.e	$4$	$8$	$4$	$7.426$	8.0.1698758656.6	None		✓			930.2.j.c	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots\)
930.2.j.d	$930$	$2$	930.j	15.e	$4$	$8$	$4$	$7.426$	\(\Q(\zeta_{24})\)	None		✓			930.2.j.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta_1 q^{2}+\beta_{2} q^{3}+\beta_{3} q^{4}+(2\beta_{5}+\beta_1)q^{5}+\cdots\)
930.2.j.e	$930$	$2$	930.j	15.e	$4$	$8$	$4$	$7.426$	\(\Q(\zeta_{24})\)	None		✓			930.2.j.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
930.2.j.f	$930$	$2$	930.j	15.e	$4$	$8$	$4$	$7.426$	8.0.1698758656.6	None		✓			930.2.j.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots\)
930.2.j.g	$930$	$2$	930.j	15.e	$4$	$40$	$20$	$7.426$		None		✓			930.2.j.g	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$
930.2.j.h	$930$	$2$	930.j	15.e	$4$	$40$	$20$	$7.426$		None		✓			930.2.j.h	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)