Properties

Label 5.19.c
Level 5
Weight 19
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 16
Newforms 1
Sturm bound 9
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 19 \)
Character orbit: \([\chi]\) = 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(5, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

\(16q \) \(\mathstrut +\mathstrut 510q^{2} \) \(\mathstrut -\mathstrut 20130q^{3} \) \(\mathstrut +\mathstrut 3145170q^{5} \) \(\mathstrut -\mathstrut 30766728q^{6} \) \(\mathstrut +\mathstrut 78767350q^{7} \) \(\mathstrut -\mathstrut 217339260q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 510q^{2} \) \(\mathstrut -\mathstrut 20130q^{3} \) \(\mathstrut +\mathstrut 3145170q^{5} \) \(\mathstrut -\mathstrut 30766728q^{6} \) \(\mathstrut +\mathstrut 78767350q^{7} \) \(\mathstrut -\mathstrut 217339260q^{8} \) \(\mathstrut -\mathstrut 635093930q^{10} \) \(\mathstrut +\mathstrut 4719921012q^{11} \) \(\mathstrut -\mathstrut 22715951880q^{12} \) \(\mathstrut +\mathstrut 8689116940q^{13} \) \(\mathstrut -\mathstrut 59706310410q^{15} \) \(\mathstrut +\mathstrut 10530345976q^{16} \) \(\mathstrut -\mathstrut 221748184620q^{17} \) \(\mathstrut +\mathstrut 654304109970q^{18} \) \(\mathstrut -\mathstrut 878373508140q^{20} \) \(\mathstrut +\mathstrut 1431507507492q^{21} \) \(\mathstrut +\mathstrut 2209421844320q^{22} \) \(\mathstrut -\mathstrut 3507966822690q^{23} \) \(\mathstrut +\mathstrut 10464353188900q^{25} \) \(\mathstrut -\mathstrut 23324455191468q^{26} \) \(\mathstrut +\mathstrut 11679867134280q^{27} \) \(\mathstrut +\mathstrut 8077754165240q^{28} \) \(\mathstrut -\mathstrut 80865025845360q^{30} \) \(\mathstrut +\mathstrut 53033402941772q^{31} \) \(\mathstrut +\mathstrut 20394786468360q^{32} \) \(\mathstrut -\mathstrut 4953707733660q^{33} \) \(\mathstrut -\mathstrut 82375887392730q^{35} \) \(\mathstrut +\mathstrut 263454471040956q^{36} \) \(\mathstrut -\mathstrut 29247362581160q^{37} \) \(\mathstrut +\mathstrut 391580910829560q^{38} \) \(\mathstrut -\mathstrut 918259855204500q^{40} \) \(\mathstrut -\mathstrut 717170436410748q^{41} \) \(\mathstrut +\mathstrut 1119760897992480q^{42} \) \(\mathstrut +\mathstrut 1295649718427950q^{43} \) \(\mathstrut -\mathstrut 2413910465914410q^{45} \) \(\mathstrut -\mathstrut 6165422784262408q^{46} \) \(\mathstrut +\mathstrut 5324712362382270q^{47} \) \(\mathstrut +\mathstrut 7675815427929360q^{48} \) \(\mathstrut -\mathstrut 10266398091964350q^{50} \) \(\mathstrut -\mathstrut 5996743906200468q^{51} \) \(\mathstrut +\mathstrut 5457051468349900q^{52} \) \(\mathstrut +\mathstrut 25019175284457720q^{53} \) \(\mathstrut -\mathstrut 28447209909214060q^{55} \) \(\mathstrut -\mathstrut 22879869030140400q^{56} \) \(\mathstrut +\mathstrut 26327201869272960q^{57} \) \(\mathstrut +\mathstrut 72036625362175440q^{58} \) \(\mathstrut -\mathstrut 129993967558538280q^{60} \) \(\mathstrut -\mathstrut 55112667981951388q^{61} \) \(\mathstrut +\mathstrut 98952816959518920q^{62} \) \(\mathstrut +\mathstrut 129200567352114030q^{63} \) \(\mathstrut -\mathstrut 145786436727900960q^{65} \) \(\mathstrut -\mathstrut 217789774433419296q^{66} \) \(\mathstrut +\mathstrut 132604737823930030q^{67} \) \(\mathstrut +\mathstrut 291394918710173220q^{68} \) \(\mathstrut -\mathstrut 344767752141139080q^{70} \) \(\mathstrut -\mathstrut 148288220084109108q^{71} \) \(\mathstrut +\mathstrut 428373837658219140q^{72} \) \(\mathstrut +\mathstrut 357896091854250160q^{73} \) \(\mathstrut -\mathstrut 656924515001553450q^{75} \) \(\mathstrut -\mathstrut 254554257141486000q^{76} \) \(\mathstrut +\mathstrut 201286979542193700q^{77} \) \(\mathstrut +\mathstrut 866949362074211400q^{78} \) \(\mathstrut -\mathstrut 608571216720410880q^{80} \) \(\mathstrut -\mathstrut 330578957555881164q^{81} \) \(\mathstrut -\mathstrut 167911799138733280q^{82} \) \(\mathstrut +\mathstrut 314012877447835830q^{83} \) \(\mathstrut -\mathstrut 37755360901186580q^{85} \) \(\mathstrut -\mathstrut 149686440788368488q^{86} \) \(\mathstrut +\mathstrut 359090097519437040q^{87} \) \(\mathstrut -\mathstrut 966828856938988320q^{88} \) \(\mathstrut +\mathstrut 2368537241357586390q^{90} \) \(\mathstrut +\mathstrut 498102030062089052q^{91} \) \(\mathstrut -\mathstrut 1299658879961370120q^{92} \) \(\mathstrut -\mathstrut 3025937916654554460q^{93} \) \(\mathstrut +\mathstrut 2986575636848949000q^{95} \) \(\mathstrut +\mathstrut 3531977749160666592q^{96} \) \(\mathstrut -\mathstrut 1689002222572272080q^{97} \) \(\mathstrut -\mathstrut 4330619740553781090q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.19.c.a \(16\) \(10.269\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(510\) \(-20130\) \(3145170\) \(78767350\) \(q+(2^{5}+\beta _{2}+2^{5}\beta _{4})q^{2}+(-1259-5\beta _{1}+\cdots)q^{3}+\cdots\)