Space of modular forms of level 7, weight 14, and trivial character

• Label: 7.14.a
• Level: $7$
• Weight: $14$
• Character orbit: 7.a
• Rep. character: $\chi_{7}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $9$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(9\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(7))\).

	Total	New	Old
Modular forms	9	7	2
Cusp forms	7	7	0
Eisenstein series	2	0	2

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

\(7\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(5\)	\(4\)	\(1\)		\(4\)	\(4\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

7 * q - q^2 - 1460 * q^3 + 16201 * q^4 + 106 * q^5 - 249730 * q^6 + 117649 * q^7 + 1044111 * q^8 + 5054923 * q^9 - 4291116 * q^10 + 2857396 * q^11 - 11853226 * q^12 + 35067410 * q^13 - 6235397 * q^14 + 42641608 * q^15 - 70787999 * q^16 - 296538162 * q^17 + 265106807 * q^18 + 100127756 * q^19 - 484624168 * q^20 + 250827668 * q^21 - 56476632 * q^22 - 466812648 * q^23 + 138302706 * q^24 + 2516838313 * q^25 + 8037344 * q^26 + 1260483688 * q^27 - 2247448847 * q^28 - 3511414046 * q^29 + 9872580752 * q^30 + 1288722704 * q^31 - 7163253329 * q^32 - 4536243872 * q^33 - 19383439710 * q^34 + 5679858422 * q^35 - 11782279063 * q^36 - 1276057126 * q^37 + 41844013970 * q^38 + 34805744008 * q^39 - 87815278704 * q^40 + 50385683558 * q^41 + 38600872198 * q^42 - 30613211020 * q^43 + 18787529696 * q^44 - 13030812110 * q^45 + 154262319312 * q^46 - 226229802336 * q^47 - 129952322722 * q^48 + 96889010407 * q^49 - 85042830131 * q^50 + 540969514392 * q^51 + 197802138884 * q^52 + 312281584170 * q^53 - 1391228853148 * q^54 - 316488210936 * q^55 + 254614906959 * q^56 - 1327058247632 * q^57 + 862061772654 * q^58 + 1195068887652 * q^59 + 2414550917408 * q^60 - 1873624454638 * q^61 - 1223389591380 * q^62 + 626763870845 * q^63 - 2172786453023 * q^64 + 2288882617420 * q^65 + 2486506773152 * q^66 + 2538837958940 * q^67 - 6452122841850 * q^68 - 2098833906384 * q^69 + 2267313174756 * q^70 - 1345886987256 * q^71 + 6129349036095 * q^72 - 29761152586 * q^73 + 6310763859270 * q^74 - 14333010265180 * q^75 - 277517688406 * q^76 + 2533628157116 * q^77 - 9665573902600 * q^78 + 4542002322080 * q^79 + 7621626949184 * q^80 + 10542390353551 * q^81 - 17646868225518 * q^82 - 2120922555780 * q^83 + 5387797838374 * q^84 - 2704554688428 * q^85 + 9427933224400 * q^86 + 9391216857448 * q^87 + 7768529810064 * q^88 - 9386830808186 * q^89 - 14841085492348 * q^90 + 1956344514446 * q^91 - 10869832218816 * q^92 + 12888631984416 * q^93 + 10462210346724 * q^94 - 248636160728 * q^95 - 3632105325086 * q^96 + 3330371194430 * q^97 - 13841287201 * q^98 - 11623975750940 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(7))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7
7.14.a.a	$7$	$14$	7.a	1.a	$1$	$3$	$3$	$7.506$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	7.14.a.a	$1$	$1$	\(26\)	\(-1796\)	\(-24086\)	\(-352947\)		$+$	$+$	$2^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(9-\beta _{1})q^{2}+(-601+7\beta _{1}-\beta _{2})q^{3}+\cdots\)
7.14.a.b	$7$	$14$	7.a	1.a	$1$	$4$	$4$	$7.506$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	7.14.a.b	$1$	$0$	\(-27\)	\(336\)	\(24192\)	\(470596\)		$-$	$-$	$2^{2}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-7+\beta _{1})q^{2}+(84+\beta _{1}+\beta _{2})q^{3}+\cdots\)