Space of modular forms of level 14, weight 8, and trivial character

• Label: 14.8.a
• Level: $14$
• Weight: $8$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	16	4	12
Cusp forms	12	4	8
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(5\)	\(1\)	\(4\)		\(4\)	\(1\)	\(3\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(9\)	\(3\)	\(6\)		\(7\)	\(3\)	\(4\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(7\)	\(1\)	\(6\)		\(5\)	\(1\)	\(4\)		\(2\)	\(0\)	\(2\)

Trace form

4 * q + 16 * q^2 - 78 * q^3 + 256 * q^4 + 174 * q^5 + 688 * q^6 + 1024 * q^8 + 8720 * q^9 - 5776 * q^10 - 972 * q^11 - 4992 * q^12 - 3734 * q^13 + 5488 * q^14 - 41368 * q^15 + 16384 * q^16 + 516 * q^17 - 2832 * q^18 - 53098 * q^19 + 11136 * q^20 + 74774 * q^21 - 46304 * q^22 - 28152 * q^23 + 44032 * q^24 + 375120 * q^25 - 143728 * q^26 + 1548 * q^27 - 54852 * q^29 + 256832 * q^30 - 31940 * q^31 + 65536 * q^32 - 815984 * q^33 - 35648 * q^34 + 26754 * q^35 + 558080 * q^36 - 465412 * q^37 - 1008496 * q^38 + 230672 * q^39 - 369664 * q^40 + 242460 * q^41 + 148176 * q^42 + 1642172 * q^43 - 62208 * q^44 - 1189082 * q^45 - 19136 * q^46 + 1906020 * q^47 - 319488 * q^48 + 470596 * q^49 + 1039696 * q^50 - 4313924 * q^51 - 238976 * q^52 + 1400616 * q^53 + 3095584 * q^54 + 5313016 * q^55 + 351232 * q^56 - 501468 * q^57 + 970688 * q^58 - 7505418 * q^59 - 2647552 * q^60 + 734830 * q^61 - 4777696 * q^62 - 1609356 * q^63 + 1048576 * q^64 - 2132844 * q^65 - 3368576 * q^66 + 1643016 * q^67 + 33024 * q^68 + 10154464 * q^69 + 2672656 * q^70 - 692616 * q^71 - 181248 * q^72 + 1957104 * q^73 - 290752 * q^74 - 13947610 * q^75 - 3398272 * q^76 - 2012724 * q^77 + 11181568 * q^78 + 5696344 * q^79 + 712704 * q^80 + 8410712 * q^81 + 4193664 * q^82 - 901650 * q^83 + 4785536 * q^84 - 12721028 * q^85 + 12553952 * q^86 + 30574484 * q^87 - 2963456 * q^88 - 10146264 * q^89 - 42033872 * q^90 - 3108266 * q^91 - 1801728 * q^92 - 19258120 * q^93 + 3778272 * q^94 + 23488776 * q^95 + 2818048 * q^96 + 17718564 * q^97 + 1882384 * q^98 - 27165244 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(14))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7
14.8.a.a	$14$	$8$	14.a	1.a	$1$	$1$	$1$	$4.373$	\(\Q\)	None	✓	✓	✓	✓	14.8.a.a	$1$	$0$	\(-8\)	\(-82\)	\(448\)	\(-343\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-82q^{3}+2^{6}q^{4}+448q^{5}+\cdots\)
14.8.a.b	$14$	$8$	14.a	1.a	$1$	$1$	$1$	$4.373$	\(\Q\)	None	✓	✓	✓	✓	14.8.a.b	$1$	$1$	\(8\)	\(-66\)	\(-400\)	\(-343\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}-66q^{3}+2^{6}q^{4}-20^{2}q^{5}+\cdots\)
14.8.a.c	$14$	$8$	14.a	1.a	$1$	$2$	$2$	$4.373$	\(\Q(\sqrt{1969}) \)	None	✓	✓	✓	✓	14.8.a.c	$1$	$0$	\(16\)	\(70\)	\(126\)	\(686\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+8q^{2}+(35-\beta )q^{3}+2^{6}q^{4}+(63+9\beta )q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)