Space of modular forms of level 350, weight 3, and Character 350.i

• Label: 350.3.i
• Level: $350$
• Weight: $3$
• Character orbit: 350.i
• Rep. character: $\chi_{350}(199,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(350, [\chi])\).

	Total	New	Old
Modular forms	264	48	216
Cusp forms	216	48	168
Eisenstein series	48	0	48

Trace form

48 * q + 48 * q^4 - 96 * q^9 + 4 * q^11 - 64 * q^14 - 96 * q^16 + 84 * q^19 + 16 * q^21 + 48 * q^24 + 96 * q^26 + 192 * q^29 - 48 * q^31 - 384 * q^36 - 264 * q^39 - 8 * q^44 + 56 * q^46 - 232 * q^49 + 32 * q^51 + 216 * q^54 - 112 * q^56 + 504 * q^59 + 264 * q^61 - 384 * q^64 - 480 * q^66 + 568 * q^71 - 256 * q^74 - 176 * q^79 - 320 * q^81 - 152 * q^84 + 256 * q^86 + 924 * q^89 + 1252 * q^91 + 720 * q^94 + 96 * q^96 - 72 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(350, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
350.3.i.a	$350$	$3$	350.i	35.i	$6$	$8$	$4$	$9.537$	\(\Q(\zeta_{24})\)	None					14.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_{5} q^{2}+(\beta_{6}-2\beta_{5}+\cdots+\beta_1)q^{3}+\cdots\)
350.3.i.b	$350$	$3$	350.i	35.i	$6$	$16$	$8$	$9.537$	16.0.\(\cdots\).1	None					70.3.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{4}+\beta _{11})q^{2}+(-\beta _{6}+\beta _{12})q^{3}+\cdots\)
350.3.i.c	$350$	$3$	350.i	35.i	$6$	$24$	$12$	$9.537$		None		✓	✓		350.3.k.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)