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

• Label: 525.2.bc
• Level: $525$
• Weight: $2$
• Character orbit: 525.bc
• Rep. character: $\chi_{525}(82,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $160$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(160\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	368	96	272
Cusp forms	272	96	176
Eisenstein series	96	0	96

Trace form

96 * q - 8 * q^7 + 24 * q^8 + 16 * q^11 + 80 * q^16 - 4 * q^21 + 8 * q^22 + 8 * q^23 - 48 * q^26 + 24 * q^28 - 48 * q^31 - 24 * q^32 + 36 * q^33 - 96 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 + 16 * q^51 + 108 * q^52 + 24 * q^53 + 96 * q^56 - 16 * q^57 - 4 * q^58 - 12 * q^61 - 4 * q^63 - 144 * q^66 - 8 * q^67 - 132 * q^68 + 32 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 48 * q^81 - 12 * q^82 - 88 * q^86 + 24 * q^87 + 32 * q^88 - 92 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

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.bc.a	$525$	$2$	525.bc	35.k	$12$	$8$	$2$	$4.192$	\(\Q(\zeta_{24})\)	None		✓			525.2.bc.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{3}+(-2\zeta_{24}^{2}+2\zeta_{24}^{6})q^{4}+\cdots\)
525.2.bc.b	$525$	$2$	525.bc	35.k	$12$	$8$	$2$	$4.192$	\(\Q(\zeta_{24})\)	None		✓			525.2.bc.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2\zeta_{24}-\zeta_{24}^{5})q^{2}+\zeta_{24}^{7}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
525.2.bc.c	$525$	$2$	525.bc	35.k	$12$	$24$	$6$	$4.192$		None		✓			525.2.bc.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
525.2.bc.d	$525$	$2$	525.bc	35.k	$12$	$24$	$6$	$4.192$		None		✓			525.2.bc.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
525.2.bc.e	$525$	$2$	525.bc	35.k	$12$	$32$	$8$	$4.192$		None			✓		105.2.u.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)