Space of modular forms of level 14, weight 12, and trivial character

• Label: 14.12.a
• Level: $14$
• Weight: $12$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	24	6	18
Cusp forms	20	6	14
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	Dim
\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(+\)	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(2\)

Trace form

6 * q - 486 * q^3 + 6144 * q^4 + 3874 * q^5 - 12608 * q^6 + 236810 * q^9 - 363456 * q^10 + 1323884 * q^11 - 497664 * q^12 + 2203470 * q^13 + 1075648 * q^14 + 5705912 * q^15 + 6291456 * q^16 - 1696024 * q^17 + 8028288 * q^18 + 1371822 * q^19 + 3966976 * q^20 - 16907842 * q^21 - 177792 * q^22 + 51566600 * q^23 - 12910592 * q^24 - 34525650 * q^25 - 98434880 * q^26 - 100431252 * q^27 - 97880648 * q^29 - 45829888 * q^30 + 204823500 * q^31 - 890574080 * q^33 - 63911808 * q^34 + 307601714 * q^35 + 242493440 * q^36 + 110267784 * q^37 + 415977024 * q^38 + 2580022976 * q^39 - 372178944 * q^40 - 1161081216 * q^41 + 261382464 * q^42 - 712891884 * q^43 + 1355657216 * q^44 + 3398855098 * q^45 + 722366208 * q^46 - 6223597068 * q^47 - 509607936 * q^48 + 1694851494 * q^49 - 3835608704 * q^50 + 6795792268 * q^51 + 2256353280 * q^52 + 7496822532 * q^53 - 11261453696 * q^54 - 7139455944 * q^55 + 1101463552 * q^56 - 17118924588 * q^57 + 9231563136 * q^58 - 20944130 * q^59 + 5842853888 * q^60 - 31239227502 * q^61 + 731196544 * q^62 + 9215547012 * q^63 + 6442450944 * q^64 + 14130637836 * q^65 - 12745084928 * q^66 + 17160124848 * q^67 - 1736728576 * q^68 + 15450049648 * q^69 + 2223364416 * q^70 - 13278746440 * q^71 + 8220966912 * q^72 + 51888151572 * q^73 - 14296955520 * q^74 + 28242983150 * q^75 + 1404745728 * q^76 + 6150622492 * q^77 - 13353795584 * q^78 - 42429894648 * q^79 + 4062183424 * q^80 + 8086601882 * q^81 + 35503508352 * q^82 - 47165805994 * q^83 - 17313630208 * q^84 + 22723837572 * q^85 + 27251479680 * q^86 - 82159329436 * q^87 - 182059008 * q^88 + 116340860076 * q^89 - 25887488192 * q^90 - 65994332586 * q^91 + 52804198400 * q^92 - 254334974536 * q^93 - 50402446464 * q^94 - 239833928104 * q^95 - 13220446208 * q^96 + 217462992744 * q^97 + 281841334172 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.12.a.a	$14$	$12$	14.a	1.a	$1$	$1$	$1$	$10.757$	\(\Q\)	None	✓	✓	✓	✓	14.12.a.a	$1$	$1$	\(-32\)	\(-396\)	\(7350\)	\(16807\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots\)
14.12.a.b	$14$	$12$	14.a	1.a	$1$	$1$	$1$	$10.757$	\(\Q\)	None	✓	✓	✓	✓	14.12.a.b	$1$	$1$	\(32\)	\(-90\)	\(-7480\)	\(-16807\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots\)
14.12.a.c	$14$	$12$	14.a	1.a	$1$	$2$	$2$	$10.757$	\(\Q(\sqrt{153169}) \)	None	✓	✓	✓	✓	14.12.a.c	$1$	$0$	\(-64\)	\(350\)	\(266\)	\(-33614\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots\)
14.12.a.d	$14$	$12$	14.a	1.a	$1$	$2$	$2$	$10.757$	\(\Q(\sqrt{352969}) \)	None	✓	✓	✓	✓	14.12.a.d	$1$	$0$	\(64\)	\(-350\)	\(3738\)	\(33614\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)