Space of modular forms of level 1521, weight 2, and Character 1521.i

• Label: 1521.2.i
• Level: $1521$
• Weight: $2$
• Character orbit: 1521.i
• Rep. character: $\chi_{1521}(746,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $8$
• Sturm bound: $364$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1521.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(364\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1521, [\chi])\).

	Total	New	Old
Modular forms	420	100	320
Cusp forms	308	100	208
Eisenstein series	112	0	112

Trace form

100 * q + 8 * q^7 - 108 * q^16 + 8 * q^19 - 32 * q^22 + 12 * q^34 - 12 * q^37 - 112 * q^40 + 72 * q^46 + 96 * q^55 + 92 * q^58 - 8 * q^61 - 64 * q^67 - 88 * q^70 - 4 * q^73 - 48 * q^76 + 32 * q^79 - 24 * q^85 - 16 * q^94 - 12 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1521, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1521.2.i.a	$1521$	$2$	1521.i	39.f	$4$	$4$	$2$	$12.145$	\(\Q(\zeta_{8})\)	None		✓			1521.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1521.2.i.b	$1521$	$2$	1521.i	39.f	$4$	$4$	$2$	$12.145$	\(\Q(\zeta_{8})\)	None		✓			1521.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{5}+(3+3\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1521.2.i.c	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	\(\Q(\zeta_{24})\)	None					117.2.ba.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{2}-\beta_{3} q^{4}+(-\beta_{7}-\beta_{4}+2\beta_1)q^{5}+\cdots\)
1521.2.i.d	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	\(\Q(\zeta_{24})\)	None					117.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{7}-\beta_{5})q^{2}+2\beta_{3} q^{4}+(-\beta_{7}+\beta_{5}+\beta_{2})q^{5}+\cdots\)
1521.2.i.e	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	\(\Q(\zeta_{24})\)	None					117.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta_{7}-\beta_{5})q^{2}+2\beta_{3} q^{4}+(-\beta_{7}+\beta_{5}+\beta_{2})q^{5}+\cdots\)
1521.2.i.f	$1521$	$2$	1521.i	39.f	$4$	$8$	$4$	$12.145$	\(\Q(\zeta_{24})\)	None					117.2.ba.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{2}-\beta_{3} q^{4}+(-\beta_{7}-\beta_{4}+2\beta_1)q^{5}+\cdots\)
1521.2.i.g	$1521$	$2$	1521.i	39.f	$4$	$12$	$6$	$12.145$	12.0.\(\cdots\).1	None					117.2.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{9}q^{2}+(\beta _{3}-2\beta _{4})q^{4}-\beta _{8}q^{5}+(1+\cdots)q^{7}+\cdots\)
1521.2.i.h	$1521$	$2$	1521.i	39.f	$4$	$48$	$24$	$12.145$		None		✓	✓		1521.2.i.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1521, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)