Space of modular forms of level 14, weight 5, and Character 14.b

• Label: 14.5.b
• Level: $14$
• Weight: $5$
• Character orbit: 14.b
• Rep. character: $\chi_{14}(13,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

	Total	New	Old
Modular forms	10	4	6
Cusp forms	6	4	2
Eisenstein series	4	0	4

Trace form

4 * q + 32 * q^4 - 76 * q^7 - 252 * q^9 + 360 * q^11 - 288 * q^14 + 384 * q^15 + 256 * q^16 + 192 * q^18 + 768 * q^21 - 1152 * q^22 - 792 * q^23 - 2300 * q^25 - 608 * q^28 + 1224 * q^29 + 4416 * q^30 + 4032 * q^35 - 2016 * q^36 - 3896 * q^37 - 768 * q^39 - 4800 * q^42 + 3688 * q^43 + 2880 * q^44 + 3072 * q^46 - 1532 * q^49 - 7488 * q^50 - 11136 * q^51 + 5832 * q^53 - 2304 * q^56 + 12864 * q^57 + 7296 * q^58 + 3072 * q^60 + 3060 * q^63 + 2048 * q^64 - 4032 * q^65 - 1048 * q^67 - 1344 * q^70 - 21528 * q^71 + 1536 * q^72 - 3456 * q^74 + 3528 * q^77 + 4800 * q^78 + 12776 * q^79 - 29628 * q^81 + 6144 * q^84 + 16512 * q^85 - 11520 * q^86 - 9216 * q^88 + 5568 * q^91 - 6336 * q^92 + 38016 * q^93 + 36864 * q^95 + 21888 * q^98 - 29592 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.5.b.a	$14$	$5$	14.b	7.b	$2$	$4$	$4$	$1.447$	4.0.1308672.3	None		✓	✓	✓	14.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-76\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)