Space of modular forms of level 90, weight 12, and Character 90.c

• Label: 90.12.c
• Level: $90$
• Weight: $12$
• Character orbit: 90.c
• Rep. character: $\chi_{90}(19,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(90, [\chi])\).

	Total	New	Old
Modular forms	206	28	178
Cusp forms	190	28	162
Eisenstein series	16	0	16

Trace form

28 * q - 28672 * q^4 + 4446 * q^5 - 28096 * q^10 - 658620 * q^11 + 4663296 * q^14 + 29360128 * q^16 + 7709928 * q^19 - 4552704 * q^20 - 81876072 * q^25 - 53324928 * q^26 - 72925164 * q^29 + 83419120 * q^31 + 185599616 * q^34 + 29153556 * q^35 + 28770304 * q^40 - 2717749584 * q^41 + 674426880 * q^44 + 3311424640 * q^46 - 9365150412 * q^49 + 3799166976 * q^50 - 96478528 * q^55 - 4775215104 * q^56 + 2077040700 * q^59 + 21317613584 * q^61 - 30064771072 * q^64 + 38234467332 * q^65 - 11009085568 * q^70 - 70914238920 * q^71 + 7257589632 * q^74 - 7894966272 * q^76 - 27891079200 * q^79 + 4661968896 * q^80 + 34746385172 * q^85 - 98504064 * q^86 - 54892999008 * q^89 + 58405785576 * q^91 - 5723630720 * q^94 - 80872970904 * q^95

Decomposition of \(S_{12}^{\mathrm{new}}(90, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
90.12.c.a	$90$	$12$	90.c	5.b	$2$	$4$	$4$	$69.151$	\(\Q(i, \sqrt{1129})\)	None					30.12.c.a	$2$	$0$	\(0\)	\(0\)	\(-4950\)	\(0\)	$2^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta _{1}q^{2}-2^{10}q^{4}+(-1205-430\beta _{1}+\cdots)q^{5}+\cdots\)
90.12.c.b	$90$	$12$	90.c	5.b	$2$	$6$	$6$	$69.151$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					10.12.b.a	$2$	$0$	\(0\)	\(0\)	\(-530\)	\(0\)	$2^{19}\cdot 3^{2}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-2^{10}q^{4}+(-88+63\beta _{2}+\cdots)q^{5}+\cdots\)
90.12.c.c	$90$	$12$	90.c	5.b	$2$	$6$	$6$	$69.151$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					30.12.c.b	$2$	$0$	\(0\)	\(0\)	\(9926\)	\(0\)	$2^{7}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta _{1}q^{2}-2^{10}q^{4}+(1654-95\beta _{1}+\cdots)q^{5}+\cdots\)
90.12.c.d	$90$	$12$	90.c	5.b	$2$	$12$	$12$	$69.151$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		90.12.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{48}\cdot 3^{16}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-2^{10}q^{4}+(-5\beta _{1}+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)