Space of modular forms of level 475, weight 2, and Character 475.j

• Label: 475.2.j
• Level: $475$
• Weight: $2$
• Character orbit: 475.j
• Rep. character: $\chi_{475}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(100\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

	Total	New	Old
Modular forms	112	64	48
Cusp forms	88	56	32
Eisenstein series	24	8	16

Trace form

56 * q + 24 * q^4 + 10 * q^6 + 26 * q^9 - 20 * q^11 - 16 * q^16 + 16 * q^19 + 10 * q^21 + 26 * q^24 + 68 * q^26 - 6 * q^29 - 44 * q^31 - 22 * q^34 - 14 * q^36 - 56 * q^39 + 10 * q^41 - 30 * q^44 - 96 * q^46 + 16 * q^49 + 26 * q^51 - 12 * q^54 - 88 * q^56 - 20 * q^59 - 42 * q^61 - 72 * q^64 - 64 * q^66 + 4 * q^69 - 12 * q^71 + 24 * q^74 + 140 * q^76 + 2 * q^79 + 36 * q^81 + 108 * q^84 + 30 * q^86 - 12 * q^89 + 46 * q^91 + 8 * q^94 + 100 * q^96 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
475.2.j.a	$475$	$2$	475.j	95.i	$6$	$4$	$2$	$3.793$	\(\Q(\zeta_{12})\)	None					95.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{3}-2\beta_{2} q^{4}+2\beta_{3} q^{7}+\beta_{2} q^{9}+\cdots\)
475.2.j.b	$475$	$2$	475.j	95.i	$6$	$12$	$6$	$3.793$	12.0.\(\cdots\).1	None					95.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.j.c	$475$	$2$	475.j	95.i	$6$	$16$	$8$	$3.793$	16.0.\(\cdots\).1	None					95.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{14}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
475.2.j.d	$475$	$2$	475.j	95.i	$6$	$24$	$12$	$3.793$		None		✓	✓		475.2.e.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(475, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)