Space of modular forms of level 784, weight 2, and Character 784.bg

• Label: 784.2.bg
• Level: $784$
• Weight: $2$
• Character orbit: 784.bg
• Rep. character: $\chi_{784}(65,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $324$
• Newform subspaces: $6$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bg (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).

	Total	New	Old
Modular forms	1416	348	1068
Cusp forms	1272	324	948
Eisenstein series	144	24	120

Trace form

324 * q + 11 * q^3 - 13 * q^5 + 10 * q^7 + 12 * q^9 + 13 * q^11 - 10 * q^13 + 16 * q^15 - 13 * q^17 + 44 * q^19 - 11 * q^21 + 19 * q^23 + 6 * q^25 + 32 * q^27 - 30 * q^29 - 22 * q^31 - 23 * q^33 + 35 * q^35 - 13 * q^37 + 26 * q^39 - 2 * q^41 - 6 * q^43 - 24 * q^45 + 17 * q^47 - 20 * q^49 + 9 * q^51 - 17 * q^53 - 8 * q^55 - 3 * q^57 - 13 * q^59 - 17 * q^61 + 32 * q^63 - 12 * q^65 + 2 * q^67 - 72 * q^69 - 30 * q^71 - q^73 + 144 * q^75 - 31 * q^77 + 20 * q^79 + 41 * q^81 + 54 * q^83 - 20 * q^85 + 40 * q^87 - q^89 - 46 * q^91 - 6 * q^93 - 16 * q^97 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
784.2.bg.a	$784$	$2$	784.bg	49.g	$21$	$24$	$2$	$6.260$		None					98.2.g.a	$2$	$0$	\(0\)	\(-7\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
784.2.bg.b	$784$	$2$	784.bg	49.g	$21$	$24$	$2$	$6.260$		None					98.2.g.b	$2$	$0$	\(0\)	\(7\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
784.2.bg.c	$784$	$2$	784.bg	49.g	$21$	$48$	$4$	$6.260$		None					49.2.g.a	$2$	$0$	\(0\)	\(14\)	\(-14\)	\(14\)		$\mathrm{SU}(2)[C_{21}]$
784.2.bg.d	$784$	$2$	784.bg	49.g	$21$	$60$	$5$	$6.260$		None					196.2.m.a	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-4\)		$\mathrm{SU}(2)[C_{21}]$
784.2.bg.e	$784$	$2$	784.bg	49.g	$21$	$84$	$7$	$6.260$		None					392.2.y.b	$2$	$0$	\(0\)	\(-10\)	\(-1\)	\(4\)		$\mathrm{SU}(2)[C_{21}]$
784.2.bg.f	$784$	$2$	784.bg	49.g	$21$	$84$	$7$	$6.260$		None					392.2.y.a	$2$	$0$	\(0\)	\(8\)	\(-1\)	\(-4\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(784, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)