Space of modular forms of level 5, weight 14, and trivial character

• Label: 5.14.a
• Level: $5$
• Weight: $14$
• Character orbit: 5.a
• Rep. character: $\chi_{5}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $7$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(7\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(5))\).

	Total	New	Old
Modular forms	7	5	2
Cusp forms	5	5	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.

\(5\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

5 * q + 62 * q^2 + 1196 * q^3 + 20660 * q^4 + 15625 * q^5 - 102440 * q^6 - 168008 * q^7 + 1846920 * q^8 + 701065 * q^9 + 3468750 * q^10 - 9071140 * q^11 - 7307408 * q^12 - 26984114 * q^13 + 4212720 * q^14 - 5687500 * q^15 + 148958480 * q^16 + 83763002 * q^17 - 157042234 * q^18 - 276572300 * q^19 + 235812500 * q^20 - 115640040 * q^21 + 829250184 * q^22 + 938237976 * q^23 - 3486583200 * q^24 + 1220703125 * q^25 - 1878546940 * q^26 + 6840734120 * q^27 - 9175428416 * q^28 - 5558962250 * q^29 + 5362375000 * q^30 + 2525174560 * q^31 + 47124742432 * q^32 - 15740664128 * q^33 - 46563846180 * q^34 + 16634250000 * q^35 - 32219390620 * q^36 + 53280246022 * q^37 - 20522011720 * q^38 - 93194383720 * q^39 + 51778125000 * q^40 - 5187070790 * q^41 + 183672177984 * q^42 - 35580322844 * q^43 - 172747838480 * q^44 + 29237078125 * q^45 + 69937838160 * q^46 + 124790088032 * q^47 - 182851529024 * q^48 - 83814315 * q^49 + 15136718750 * q^50 + 66506371960 * q^51 - 179398257128 * q^52 + 45099752246 * q^53 + 536511689200 * q^54 - 64638562500 * q^55 - 390912048000 * q^56 - 993398437360 * q^57 + 876855259620 * q^58 + 198065183900 * q^59 - 627148250000 * q^60 + 118702152910 * q^61 - 1356767292096 * q^62 + 1021221430056 * q^63 + 2904548125760 * q^64 - 625309906250 * q^65 + 1349455452320 * q^66 - 1916484488948 * q^67 - 702944699096 * q^68 + 1733326708680 * q^69 - 1520915250000 * q^70 - 34192224440 * q^71 - 4905432210840 * q^72 + 1948560188626 * q^73 - 109439689580 * q^74 + 291992187500 * q^75 - 461694974000 * q^76 + 2438453692944 * q^77 - 1260878170928 * q^78 + 582406315600 * q^79 + 3919780250000 * q^80 - 2260323371195 * q^81 + 5711708077164 * q^82 + 1238839864716 * q^83 - 7123955940480 * q^84 + 1289001281250 * q^85 + 3739127986760 * q^86 + 7315958847560 * q^87 - 12297158950560 * q^88 - 19316178282750 * q^89 + 1485537593750 * q^90 - 5317987188640 * q^91 + 39896707925952 * q^92 - 1545330136368 * q^93 - 15675401986080 * q^94 + 7368039062500 * q^95 + 6170892824960 * q^96 + 7656084054682 * q^97 - 27831437745266 * q^98 - 10958886660820 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(5))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5
5.14.a.a	$5$	$14$	5.a	1.a	$1$	$2$	$2$	$5.362$	\(\Q(\sqrt{499}) \)	None	✓	✓	✓	✓	5.14.a.a	$1$	$1$	\(-80\)	\(780\)	\(-31250\)	\(-616300\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-40+\beta )q^{2}+(390-12\beta )q^{3}+(1392+\cdots)q^{4}+\cdots\)
5.14.a.b	$5$	$14$	5.a	1.a	$1$	$3$	$3$	$5.362$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	5.14.a.b	$1$	$0$	\(142\)	\(416\)	\(46875\)	\(448292\)		$-$	$-$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(47-\beta _{1})q^{2}+(138-3\beta _{1}-\beta _{2})q^{3}+\cdots\)