Space of modular forms of level 555, weight 2, and Character 555.c

• Label: 555.2.c
• Level: $555$
• Weight: $2$
• Character orbit: 555.c
• Rep. character: $\chi_{555}(334,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $152$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(152\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(555, [\chi])\).

	Total	New	Old
Modular forms	80	36	44
Cusp forms	72	36	36
Eisenstein series	8	0	8

Trace form

36 * q - 32 * q^4 - 4 * q^5 - 36 * q^9 + 8 * q^11 - 8 * q^14 + 24 * q^16 - 16 * q^19 + 8 * q^20 + 20 * q^25 + 24 * q^26 - 16 * q^29 + 24 * q^31 + 8 * q^34 - 4 * q^35 + 32 * q^36 - 16 * q^39 - 16 * q^40 - 16 * q^44 + 4 * q^45 - 8 * q^46 - 68 * q^49 - 44 * q^50 + 8 * q^51 + 24 * q^55 + 72 * q^56 + 40 * q^59 - 4 * q^60 + 8 * q^61 - 32 * q^64 - 24 * q^65 + 32 * q^66 - 8 * q^69 - 64 * q^70 - 24 * q^71 + 8 * q^75 + 112 * q^76 - 64 * q^79 - 88 * q^80 + 36 * q^81 - 16 * q^84 - 16 * q^85 + 112 * q^86 + 40 * q^91 - 32 * q^94 + 24 * q^95 - 40 * q^96 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(555, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
555.2.c.a	$555$	$2$	555.c	5.b	$2$	$2$	$2$	$4.432$	\(\Q(\sqrt{-1}) \)	None		✓			555.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}+(2 i-1)q^{5}+\cdots\)
555.2.c.b	$555$	$2$	555.c	5.b	$2$	$8$	$8$	$4.432$	8.0.309760000.3	None		✓			555.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
555.2.c.c	$555$	$2$	555.c	5.b	$2$	$26$	$26$	$4.432$		None		✓	✓		555.2.c.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(555, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(555, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)