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

• Label: 930.2.d
• Level: $930$
• Weight: $2$
• Character orbit: 930.d
• Rep. character: $\chi_{930}(559,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $9$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	200	28	172
Cusp forms	184	28	156
Eisenstein series	16	0	16

Trace form

28 * q - 28 * q^4 + 8 * q^5 - 28 * q^9 - 8 * q^11 - 8 * q^14 - 8 * q^15 + 28 * q^16 + 16 * q^19 - 8 * q^20 + 24 * q^26 - 16 * q^29 - 16 * q^34 + 28 * q^36 + 24 * q^41 + 8 * q^44 - 8 * q^45 + 8 * q^46 - 20 * q^49 - 16 * q^50 + 8 * q^51 - 24 * q^55 + 8 * q^56 + 24 * q^59 + 8 * q^60 - 28 * q^64 - 40 * q^65 - 16 * q^66 + 16 * q^69 + 32 * q^71 - 8 * q^74 + 32 * q^75 - 16 * q^76 - 48 * q^79 + 8 * q^80 + 28 * q^81 - 24 * q^85 + 16 * q^86 - 72 * q^89 + 32 * q^91 + 56 * q^94 - 24 * q^95 + 8 * q^99

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.d.a	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		✓			930.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}+(2 i-1)q^{5}+\cdots\)
930.2.d.b	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		✓			930.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots\)
930.2.d.c	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		✓			930.2.d.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+(2 i+1)q^{5}+\cdots\)
930.2.d.d	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		✓			930.2.d.d	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}+(i+2)q^{5}+\cdots\)
930.2.d.e	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		✓			930.2.d.e	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+(i+2)q^{5}+\cdots\)
930.2.d.f	$930$	$2$	930.d	5.b	$2$	$2$	$2$	$7.426$	\(\Q(\sqrt{-1}) \)	None		✓			930.2.d.f	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+(-i+2)q^{5}+\cdots\)
930.2.d.g	$930$	$2$	930.d	5.b	$2$	$4$	$4$	$7.426$	\(\Q(\zeta_{8})\)	None		✓			930.2.d.g	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+\beta_1 q^{3}-q^{4}+(\beta_1+2)q^{5}+\cdots\)
930.2.d.h	$930$	$2$	930.d	5.b	$2$	$6$	$6$	$7.426$	6.0.3534400.1	None		✓			930.2.d.h	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
930.2.d.i	$930$	$2$	930.d	5.b	$2$	$6$	$6$	$7.426$	6.0.11669056.1	None		✓			930.2.d.i	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)