Properties

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 $1$

Related objects

Downloads

Learn more

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.

\(5\)Dim.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\( 5 q + 62 q^{2} + 1196 q^{3} + 20660 q^{4} + 15625 q^{5} - 102440 q^{6} - 168008 q^{7} + 1846920 q^{8} + 701065 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.14.a.a 5.a 1.a $2$ $5.362$ \(\Q(\sqrt{499}) \) None \(-80\) \(780\) \(-31250\) \(-616300\) $+$ $\mathrm{SU}(2)$ \(q+(-40+\beta )q^{2}+(390-12\beta )q^{3}+(1392+\cdots)q^{4}+\cdots\)
5.14.a.b 5.a 1.a $3$ $5.362$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(142\) \(416\) \(46875\) \(448292\) $-$ $\mathrm{SU}(2)$ \(q+(47-\beta _{1})q^{2}+(138-3\beta _{1}-\beta _{2})q^{3}+\cdots\)