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

• Label: 14.14.a
• Level: $14$
• Weight: $14$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $28$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	28	6	22
Cusp forms	24	6	18
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
\(+\)	\(+\)	\(+\)		\(6\)	\(1\)	\(5\)		\(5\)	\(1\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(8\)	\(2\)	\(6\)		\(7\)	\(2\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(7\)	\(2\)	\(5\)		\(6\)	\(2\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(7\)	\(1\)	\(6\)		\(6\)	\(1\)	\(5\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(13\)	\(2\)	\(11\)		\(11\)	\(2\)	\(9\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(15\)	\(4\)	\(11\)		\(13\)	\(4\)	\(9\)		\(2\)	\(0\)	\(2\)

Trace form

6 * q + 2658 * q^3 + 24576 * q^4 + 75454 * q^5 - 159872 * q^6 - 54334 * q^9 + 5391744 * q^10 - 4198900 * q^11 + 10887168 * q^12 - 21536910 * q^13 - 15059072 * q^14 + 74652440 * q^15 + 100663296 * q^16 + 127703888 * q^17 + 109790976 * q^18 + 356289702 * q^19 + 309059584 * q^20 - 330123094 * q^21 - 429056256 * q^22 + 2583845000 * q^23 - 654835712 * q^24 + 803490486 * q^25 - 211760000 * q^26 + 2993080284 * q^27 - 116007344 * q^29 + 3944153600 * q^30 - 16892503572 * q^31 - 4033651040 * q^33 - 2957779200 * q^34 - 330123094 * q^35 - 222552064 * q^36 - 6687870048 * q^37 - 20960621952 * q^38 - 83596016032 * q^39 + 22084583424 * q^40 + 63713977272 * q^41 - 10978063488 * q^42 - 77765105388 * q^43 - 17198694400 * q^44 + 62435143798 * q^45 - 4846932480 * q^46 + 372645466836 * q^47 + 44593840128 * q^48 + 83047723206 * q^49 - 121923762944 * q^50 - 269390050820 * q^51 - 88215183360 * q^52 - 255705729036 * q^53 + 519469197568 * q^54 + 317621938296 * q^55 - 61681958912 * q^56 + 395214315276 * q^57 + 69342181632 * q^58 - 712642478042 * q^59 + 305776394240 * q^60 + 1774004468670 * q^61 - 196641183488 * q^62 - 576231154716 * q^63 + 412316860416 * q^64 - 2223781083804 * q^65 - 1854843428864 * q^66 - 3537401376576 * q^67 + 523075125248 * q^68 + 1675209451120 * q^69 - 1051228639104 * q^70 + 2331418655096 * q^71 + 449703837696 * q^72 - 1394414740956 * q^73 - 2823317149440 * q^74 + 6299688623990 * q^75 + 1459362619392 * q^76 - 1891936628204 * q^77 + 2281850355712 * q^78 - 4214235906456 * q^79 + 1265908056064 * q^80 - 5400214549582 * q^81 + 1312824627456 * q^82 - 2760602952178 * q^83 - 1352184193024 * q^84 + 13991004814908 * q^85 + 258030341376 * q^86 + 5224716578852 * q^87 - 1757414424576 * q^88 + 11243600567052 * q^89 + 6698734949248 * q^90 - 1445221257522 * q^91 + 10583429120000 * q^92 - 25415783886232 * q^93 - 9467660368128 * q^94 + 20345555963960 * q^95 - 2682207076352 * q^96 - 10215598221168 * q^97 - 10722640750564 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.14.a.a	$14$	$14$	14.a	1.a	$1$	$1$	$1$	$15.012$	\(\Q\)	None	✓	✓	✓	✓	14.14.a.a	$1$	$1$	\(-64\)	\(1626\)	\(-36400\)	\(-117649\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+1626q^{3}+2^{12}q^{4}-36400q^{5}+\cdots\)
14.14.a.b	$14$	$14$	14.a	1.a	$1$	$1$	$1$	$15.012$	\(\Q\)	None	✓	✓	✓	✓	14.14.a.b	$1$	$1$	\(64\)	\(-1026\)	\(4320\)	\(117649\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}-1026q^{3}+2^{12}q^{4}+4320q^{5}+\cdots\)
14.14.a.c	$14$	$14$	14.a	1.a	$1$	$2$	$2$	$15.012$	\(\Q(\sqrt{100129}) \)	None	✓	✓	✓	✓	14.14.a.c	$1$	$0$	\(-128\)	\(952\)	\(32004\)	\(235298\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}+(476-\beta )q^{3}+2^{12}q^{4}+(16002+\cdots)q^{5}+\cdots\)
14.14.a.d	$14$	$14$	14.a	1.a	$1$	$2$	$2$	$15.012$	\(\Q(\sqrt{78985}) \)	None	✓	✓	✓	✓	14.14.a.d	$1$	$0$	\(128\)	\(1106\)	\(75530\)	\(-235298\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+(553-5\beta )q^{3}+2^{12}q^{4}+\cdots\)

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

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