Space of modular forms of level 14, weight 10, and trivial character

• Label: 14.10.a
• Level: $14$
• Weight: $10$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	20	4	16
Cusp forms	16	4	12
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
\(+\)	\(+\)	\(+\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(6\)	\(2\)	\(4\)		\(5\)	\(2\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(5\)	\(1\)	\(4\)		\(4\)	\(1\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(9\)	\(1\)	\(8\)		\(7\)	\(1\)	\(6\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(11\)	\(3\)	\(8\)		\(9\)	\(3\)	\(6\)		\(2\)	\(0\)	\(2\)

Trace form

4 * q - 32 * q^2 + 150 * q^3 + 1024 * q^4 - 1626 * q^5 + 3040 * q^6 - 8192 * q^8 + 65552 * q^9 + 43424 * q^10 + 39612 * q^11 + 38400 * q^12 - 28766 * q^13 - 76832 * q^14 + 592280 * q^15 + 262144 * q^16 - 885564 * q^17 - 753888 * q^18 + 49442 * q^19 - 416256 * q^20 - 427378 * q^21 + 928576 * q^22 - 2656200 * q^23 + 778240 * q^24 - 1443504 * q^25 - 47776 * q^26 - 3413052 * q^27 + 9137868 * q^29 - 6517120 * q^30 + 3350596 * q^31 - 2097152 * q^32 + 32512912 * q^33 + 13483648 * q^34 - 9205434 * q^35 + 16781312 * q^36 - 36564244 * q^37 - 23716192 * q^38 - 7908112 * q^39 + 11116544 * q^40 + 34564860 * q^41 - 6223392 * q^42 + 13013012 * q^43 + 10140672 * q^44 - 116480402 * q^45 - 36540800 * q^46 + 34924380 * q^47 + 9830400 * q^48 + 23059204 * q^49 - 29933984 * q^50 - 34235276 * q^51 - 7364096 * q^52 - 46913208 * q^53 - 2326208 * q^54 + 36542536 * q^55 - 19668992 * q^56 + 183244164 * q^57 + 31612544 * q^58 - 108522318 * q^59 + 151623680 * q^60 + 76257142 * q^61 + 131969600 * q^62 + 207475212 * q^63 + 67108864 * q^64 - 230680044 * q^65 - 254604032 * q^66 + 580211352 * q^67 - 226704384 * q^68 - 254285600 * q^69 + 105490336 * q^70 + 16036680 * q^71 - 192995328 * q^72 - 142210704 * q^73 + 460406144 * q^74 - 1606313950 * q^75 + 12657152 * q^76 + 120693468 * q^77 + 40164352 * q^78 + 635427112 * q^79 - 106561536 * q^80 + 540236888 * q^81 - 756585216 * q^82 - 134458710 * q^83 - 109408768 * q^84 + 1026034348 * q^85 - 806649664 * q^86 - 1833076660 * q^87 + 237715456 * q^88 + 156632808 * q^89 + 2024135968 * q^90 + 550621330 * q^91 - 679987200 * q^92 + 91836440 * q^93 + 1250460096 * q^94 + 362338680 * q^95 + 199229440 * q^96 - 118654428 * q^97 - 184473632 * q^98 + 2882415692 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.10.a.a	$14$	$10$	14.a	1.a	$1$	$1$	$1$	$7.211$	\(\Q\)	None	✓	✓	✓	✓	14.10.a.a	$1$	$1$	\(-16\)	\(-6\)	\(560\)	\(-2401\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots\)
14.10.a.b	$14$	$10$	14.a	1.a	$1$	$1$	$1$	$7.211$	\(\Q\)	None	✓	✓	✓	✓	14.10.a.b	$1$	$0$	\(16\)	\(170\)	\(544\)	\(-2401\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots\)
14.10.a.c	$14$	$10$	14.a	1.a	$1$	$2$	$2$	$7.211$	\(\Q(\sqrt{2305}) \)	None	✓	✓	✓	✓	14.10.a.c	$1$	$0$	\(-32\)	\(-14\)	\(-2730\)	\(4802\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)