Space of modular forms of level 258, weight 2, and Character 258.d

• Label: 258.2.d
• Level: $258$
• Weight: $2$
• Character orbit: 258.d
• Rep. character: $\chi_{258}(257,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $88$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 258 = 2 \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	258.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(88\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(258, [\chi])\).

	Total	New	Old
Modular forms	48	16	32
Cusp forms	40	16	24
Eisenstein series	8	0	8

Trace form

16 * q + 16 * q^4 - 6 * q^6 + 6 * q^9 - 20 * q^13 + 16 * q^16 - 6 * q^24 + 16 * q^25 - 20 * q^31 + 6 * q^36 - 28 * q^43 - 20 * q^49 - 20 * q^52 - 6 * q^54 + 16 * q^64 - 12 * q^66 - 56 * q^67 - 12 * q^78 - 20 * q^79 + 6 * q^81 - 30 * q^87 - 30 * q^90 - 6 * q^96 + 32 * q^97 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(258, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
258.2.d.a	$258$	$2$	258.d	129.d	$2$	$2$	$2$	$2.060$	\(\Q(\sqrt{-3}) \)	None		✓			258.2.d.a	$2$	$1$	\(-2\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta q^{3}+q^{4}-3 q^{5}+\beta q^{6}+\cdots\)
258.2.d.b	$258$	$2$	258.d	129.d	$2$	$2$	$2$	$2.060$	\(\Q(\sqrt{-3}) \)	None		✓			258.2.d.a	$2$	$0$	\(2\)	\(0\)	\(6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta q^{3}+q^{4}+3 q^{5}+\beta q^{6}+\cdots\)
258.2.d.c	$258$	$2$	258.d	129.d	$2$	$6$	$6$	$2.060$	6.0.5604552.1	None		✓			258.2.d.c	$2$	$0$	\(-6\)	\(3\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+(1+\beta _{3})q^{3}+q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
258.2.d.d	$258$	$2$	258.d	129.d	$2$	$6$	$6$	$2.060$	6.0.5604552.1	None		✓			258.2.d.c	$2$	$0$	\(6\)	\(-3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(258, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(258, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)