Properties

Label 19.8.a
Level 19
Weight 8
Character orbit a
Rep. character \(\chi_{19}(1,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 2
Sturm bound 13
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 19.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(13\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(19))\).

Total New Old
Modular forms 12 10 2
Cusp forms 10 10 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.

\(19\)Dim.
\(+\)\(6\)
\(-\)\(4\)

Trace form

\(10q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 394q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 322q^{6} \) \(\mathstrut +\mathstrut 859q^{7} \) \(\mathstrut +\mathstrut 2280q^{8} \) \(\mathstrut +\mathstrut 1018q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 394q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 322q^{6} \) \(\mathstrut +\mathstrut 859q^{7} \) \(\mathstrut +\mathstrut 2280q^{8} \) \(\mathstrut +\mathstrut 1018q^{9} \) \(\mathstrut +\mathstrut 1768q^{10} \) \(\mathstrut -\mathstrut 1461q^{11} \) \(\mathstrut +\mathstrut 744q^{12} \) \(\mathstrut +\mathstrut 2370q^{13} \) \(\mathstrut +\mathstrut 6924q^{14} \) \(\mathstrut +\mathstrut 890q^{15} \) \(\mathstrut +\mathstrut 10234q^{16} \) \(\mathstrut +\mathstrut 975q^{17} \) \(\mathstrut -\mathstrut 6258q^{18} \) \(\mathstrut -\mathstrut 13718q^{19} \) \(\mathstrut +\mathstrut 13608q^{20} \) \(\mathstrut -\mathstrut 49166q^{21} \) \(\mathstrut -\mathstrut 108688q^{22} \) \(\mathstrut -\mathstrut 31248q^{23} \) \(\mathstrut -\mathstrut 60978q^{24} \) \(\mathstrut -\mathstrut 77473q^{25} \) \(\mathstrut -\mathstrut 78006q^{26} \) \(\mathstrut +\mathstrut 124508q^{27} \) \(\mathstrut +\mathstrut 129054q^{28} \) \(\mathstrut +\mathstrut 127380q^{29} \) \(\mathstrut -\mathstrut 126436q^{30} \) \(\mathstrut -\mathstrut 39380q^{31} \) \(\mathstrut +\mathstrut 210096q^{32} \) \(\mathstrut +\mathstrut 134066q^{33} \) \(\mathstrut +\mathstrut 537772q^{34} \) \(\mathstrut +\mathstrut 175905q^{35} \) \(\mathstrut -\mathstrut 300692q^{36} \) \(\mathstrut +\mathstrut 811840q^{37} \) \(\mathstrut -\mathstrut 164616q^{38} \) \(\mathstrut +\mathstrut 859224q^{39} \) \(\mathstrut -\mathstrut 293364q^{40} \) \(\mathstrut -\mathstrut 343332q^{41} \) \(\mathstrut -\mathstrut 1024798q^{42} \) \(\mathstrut +\mathstrut 236159q^{43} \) \(\mathstrut -\mathstrut 1690416q^{44} \) \(\mathstrut -\mathstrut 332011q^{45} \) \(\mathstrut +\mathstrut 343556q^{46} \) \(\mathstrut +\mathstrut 88545q^{47} \) \(\mathstrut -\mathstrut 1571712q^{48} \) \(\mathstrut -\mathstrut 606421q^{49} \) \(\mathstrut -\mathstrut 1581846q^{50} \) \(\mathstrut +\mathstrut 975142q^{51} \) \(\mathstrut -\mathstrut 909908q^{52} \) \(\mathstrut +\mathstrut 3303498q^{53} \) \(\mathstrut -\mathstrut 442034q^{54} \) \(\mathstrut -\mathstrut 481635q^{55} \) \(\mathstrut +\mathstrut 2745012q^{56} \) \(\mathstrut -\mathstrut 370386q^{57} \) \(\mathstrut +\mathstrut 2661970q^{58} \) \(\mathstrut -\mathstrut 885954q^{59} \) \(\mathstrut +\mathstrut 1316620q^{60} \) \(\mathstrut +\mathstrut 932281q^{61} \) \(\mathstrut -\mathstrut 2095068q^{62} \) \(\mathstrut -\mathstrut 3233781q^{63} \) \(\mathstrut +\mathstrut 462754q^{64} \) \(\mathstrut +\mathstrut 296448q^{65} \) \(\mathstrut -\mathstrut 111604q^{66} \) \(\mathstrut -\mathstrut 3534352q^{67} \) \(\mathstrut -\mathstrut 848814q^{68} \) \(\mathstrut -\mathstrut 3319512q^{69} \) \(\mathstrut +\mathstrut 6172716q^{70} \) \(\mathstrut +\mathstrut 4767558q^{71} \) \(\mathstrut +\mathstrut 6970200q^{72} \) \(\mathstrut -\mathstrut 4576669q^{73} \) \(\mathstrut +\mathstrut 12391656q^{74} \) \(\mathstrut -\mathstrut 5252924q^{75} \) \(\mathstrut -\mathstrut 2194880q^{76} \) \(\mathstrut -\mathstrut 1691319q^{77} \) \(\mathstrut -\mathstrut 420236q^{78} \) \(\mathstrut +\mathstrut 7345288q^{79} \) \(\mathstrut +\mathstrut 14281620q^{80} \) \(\mathstrut -\mathstrut 13798874q^{81} \) \(\mathstrut -\mathstrut 2233388q^{82} \) \(\mathstrut +\mathstrut 4739088q^{83} \) \(\mathstrut -\mathstrut 16782156q^{84} \) \(\mathstrut -\mathstrut 11785041q^{85} \) \(\mathstrut +\mathstrut 2052972q^{86} \) \(\mathstrut -\mathstrut 15657084q^{87} \) \(\mathstrut -\mathstrut 19763640q^{88} \) \(\mathstrut +\mathstrut 15372558q^{89} \) \(\mathstrut +\mathstrut 5785580q^{90} \) \(\mathstrut +\mathstrut 8899364q^{91} \) \(\mathstrut -\mathstrut 15201174q^{92} \) \(\mathstrut +\mathstrut 18645168q^{93} \) \(\mathstrut -\mathstrut 20440488q^{94} \) \(\mathstrut -\mathstrut 3024819q^{95} \) \(\mathstrut -\mathstrut 7681042q^{96} \) \(\mathstrut -\mathstrut 3884078q^{97} \) \(\mathstrut +\mathstrut 57894318q^{98} \) \(\mathstrut +\mathstrut 36282547q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(19))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 19
19.8.a.a \(4\) \(5.935\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-9\) \(-14\) \(-222\) \(-1246\) \(-\) \(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots\)
19.8.a.b \(6\) \(5.935\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(15\) \(40\) \(219\) \(2105\) \(+\) \(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(57+\cdots)q^{4}+\cdots\)