Space of modular forms of level 525, weight 3, and Character 525.e

• Label: 525.3.e
• Level: $525$
• Weight: $3$
• Character orbit: 525.e
• Rep. character: $\chi_{525}(349,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).

	Total	New	Old
Modular forms	172	48	124
Cusp forms	148	48	100
Eisenstein series	24	0	24

Trace form

48 * q - 96 * q^4 + 144 * q^9 + 72 * q^11 + 108 * q^14 + 96 * q^16 - 6 * q^21 + 24 * q^29 - 288 * q^36 + 36 * q^39 - 876 * q^44 - 108 * q^46 + 54 * q^49 - 48 * q^51 - 468 * q^56 + 324 * q^64 + 192 * q^71 - 444 * q^74 - 408 * q^79 + 432 * q^81 + 24 * q^84 - 348 * q^86 + 366 * q^91 + 216 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
525.3.e.a	$525$	$3$	525.e	35.c	$2$	$4$	$4$	$14.305$	\(\Q(\zeta_{12})\)	None					21.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}-\beta_{3} q^{3}+3 q^{4}+\beta_{2} q^{6}+\cdots\)
525.3.e.b	$525$	$3$	525.e	35.c	$2$	$20$	$20$	$14.305$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			525.3.h.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-\beta _{10}q^{3}+(-1+\beta _{1})q^{4}+\cdots\)
525.3.e.c	$525$	$3$	525.e	35.c	$2$	$24$	$24$	$14.305$		None			✓		105.3.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(525, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)