Space of modular forms of level 245, weight 3, and Character 245.d

• Label: 245.3.d
• Level: $245$
• Weight: $3$
• Character orbit: 245.d
• Rep. character: $\chi_{245}(146,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	245.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(245, [\chi])\).

	Total	New	Old
Modular forms	64	28	36
Cusp forms	48	28	20
Eisenstein series	16	0	16

Trace form

28 * q - 4 * q^2 + 76 * q^4 + 4 * q^8 - 84 * q^9 - 12 * q^11 + 20 * q^15 + 164 * q^16 - 8 * q^18 + 40 * q^22 - 100 * q^23 - 140 * q^25 - 72 * q^29 - 40 * q^30 + 52 * q^32 - 364 * q^36 + 104 * q^37 - 168 * q^39 + 124 * q^43 + 20 * q^44 - 116 * q^46 + 20 * q^50 + 272 * q^51 + 24 * q^53 + 112 * q^57 - 172 * q^58 + 20 * q^60 + 140 * q^64 - 180 * q^65 + 276 * q^67 - 200 * q^71 + 160 * q^72 + 220 * q^74 + 504 * q^78 - 544 * q^79 + 364 * q^81 + 120 * q^85 + 432 * q^86 + 8 * q^88 - 596 * q^92 - 264 * q^93 + 40 * q^95 + 308 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(245, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.3.d.a	$245$	$3$	245.d	7.b	$2$	$12$	$12$	$6.676$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					35.3.h.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots\)
245.3.d.b	$245$	$3$	245.d	7.b	$2$	$16$	$16$	$6.676$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		245.3.d.b	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+\beta _{6}q^{3}+(3-\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)