Space of modular forms of level 525, weight 2, and Character 525.q

• Label: 525.2.q
• Level: $525$
• Weight: $2$
• Character orbit: 525.q
• Rep. character: $\chi_{525}(299,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $7$
• Sturm bound: $160$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(160\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

	Total	New	Old
Modular forms	184	104	80
Cusp forms	136	88	48
Eisenstein series	48	16	32

Trace form

88 * q - 36 * q^4 + 10 * q^9 - 28 * q^16 + 18 * q^19 - 72 * q^24 - 24 * q^31 - 96 * q^36 + 6 * q^39 - 56 * q^46 + 2 * q^49 + 18 * q^51 + 102 * q^54 - 78 * q^61 + 32 * q^64 - 12 * q^66 - 32 * q^79 + 14 * q^81 - 30 * q^84 + 18 * q^91 + 84 * q^94 + 234 * q^96 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
525.2.q.a	$525$	$2$	525.q	105.p	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None					105.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
525.2.q.b	$525$	$2$	525.q	105.p	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None					105.2.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
525.2.q.c	$525$	$2$	525.q	105.p	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		✓			525.2.t.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
525.2.q.d	$525$	$2$	525.q	105.p	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)					21.2.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
525.2.q.e	$525$	$2$	525.q	105.p	$6$	$16$	$8$	$4.192$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					105.2.s.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{8}+\beta _{14})q^{3}+(\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.q.f	$525$	$2$	525.q	105.p	$6$	$16$	$8$	$4.192$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					105.2.s.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{7}-\beta _{8}+\beta _{12}+\cdots)q^{3}+\cdots\)
525.2.q.g	$525$	$2$	525.q	105.p	$6$	$40$	$20$	$4.192$		None		✓	✓		525.2.t.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(525, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)