Properties

Label 4.19.b
Level 4
Weight 19
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(4, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 8 8 0
Eisenstein series 2 2 0

Trace form

\(8q \) \(\mathstrut +\mathstrut 84q^{2} \) \(\mathstrut +\mathstrut 352016q^{4} \) \(\mathstrut +\mathstrut 860880q^{5} \) \(\mathstrut +\mathstrut 310944q^{6} \) \(\mathstrut -\mathstrut 154160064q^{8} \) \(\mathstrut -\mathstrut 729541560q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 84q^{2} \) \(\mathstrut +\mathstrut 352016q^{4} \) \(\mathstrut +\mathstrut 860880q^{5} \) \(\mathstrut +\mathstrut 310944q^{6} \) \(\mathstrut -\mathstrut 154160064q^{8} \) \(\mathstrut -\mathstrut 729541560q^{9} \) \(\mathstrut -\mathstrut 853591160q^{10} \) \(\mathstrut -\mathstrut 2983758720q^{12} \) \(\mathstrut -\mathstrut 6658778288q^{13} \) \(\mathstrut -\mathstrut 3330240576q^{14} \) \(\mathstrut +\mathstrut 35282993408q^{16} \) \(\mathstrut +\mathstrut 213854181648q^{17} \) \(\mathstrut +\mathstrut 197420552436q^{18} \) \(\mathstrut -\mathstrut 421824543840q^{20} \) \(\mathstrut -\mathstrut 771822339072q^{21} \) \(\mathstrut -\mathstrut 586750684320q^{22} \) \(\mathstrut -\mathstrut 3940602195456q^{24} \) \(\mathstrut +\mathstrut 528925732440q^{25} \) \(\mathstrut +\mathstrut 12314194404552q^{26} \) \(\mathstrut -\mathstrut 20860043224320q^{28} \) \(\mathstrut +\mathstrut 11238056568912q^{29} \) \(\mathstrut +\mathstrut 63814514963520q^{30} \) \(\mathstrut -\mathstrut 133632603995136q^{32} \) \(\mathstrut -\mathstrut 21541938424320q^{33} \) \(\mathstrut +\mathstrut 295093712425768q^{34} \) \(\mathstrut -\mathstrut 595880470532208q^{36} \) \(\mathstrut -\mathstrut 158886968816432q^{37} \) \(\mathstrut +\mathstrut 830666716492320q^{38} \) \(\mathstrut -\mathstrut 1609388875268480q^{40} \) \(\mathstrut +\mathstrut 451509984725136q^{41} \) \(\mathstrut +\mathstrut 3247297173265920q^{42} \) \(\mathstrut -\mathstrut 3429204744604800q^{44} \) \(\mathstrut +\mathstrut 394282398204240q^{45} \) \(\mathstrut +\mathstrut 3658225092496704q^{46} \) \(\mathstrut -\mathstrut 6713415182530560q^{48} \) \(\mathstrut -\mathstrut 2251201133570680q^{49} \) \(\mathstrut +\mathstrut 6942506471898780q^{50} \) \(\mathstrut -\mathstrut 6479715597253472q^{52} \) \(\mathstrut +\mathstrut 1216384760086992q^{53} \) \(\mathstrut +\mathstrut 3284600487812928q^{54} \) \(\mathstrut +\mathstrut 7432202560564224q^{56} \) \(\mathstrut +\mathstrut 2661563378188800q^{57} \) \(\mathstrut -\mathstrut 17440122911455928q^{58} \) \(\mathstrut +\mathstrut 36392091128935680q^{60} \) \(\mathstrut +\mathstrut 184592915104336q^{61} \) \(\mathstrut -\mathstrut 42580340982416640q^{62} \) \(\mathstrut +\mathstrut 74097564160495616q^{64} \) \(\mathstrut -\mathstrut 5670291051587040q^{65} \) \(\mathstrut -\mathstrut 140809597617788160q^{66} \) \(\mathstrut +\mathstrut 131212356714741792q^{68} \) \(\mathstrut -\mathstrut 26839260584143872q^{69} \) \(\mathstrut -\mathstrut 153862868594448000q^{70} \) \(\mathstrut +\mathstrut 156072744876684864q^{72} \) \(\mathstrut +\mathstrut 31494366486758032q^{73} \) \(\mathstrut -\mathstrut 108949653815722872q^{74} \) \(\mathstrut +\mathstrut 152098090223483520q^{76} \) \(\mathstrut +\mathstrut 180811187963888640q^{77} \) \(\mathstrut +\mathstrut 14085206442507840q^{78} \) \(\mathstrut -\mathstrut 152292076037383680q^{80} \) \(\mathstrut -\mathstrut 260466732987857784q^{81} \) \(\mathstrut +\mathstrut 335145451981844968q^{82} \) \(\mathstrut -\mathstrut 850166994683553792q^{84} \) \(\mathstrut -\mathstrut 204660361893474400q^{85} \) \(\mathstrut +\mathstrut 950236163482864224q^{86} \) \(\mathstrut -\mathstrut 1369014843355476480q^{88} \) \(\mathstrut +\mathstrut 162001265029847952q^{89} \) \(\mathstrut +\mathstrut 1771450132254688200q^{90} \) \(\mathstrut -\mathstrut 1193579560451823360q^{92} \) \(\mathstrut +\mathstrut 668158876340367360q^{93} \) \(\mathstrut +\mathstrut 1478730179820369024q^{94} \) \(\mathstrut -\mathstrut 2028358051400441856q^{96} \) \(\mathstrut -\mathstrut 1214976752903766512q^{97} \) \(\mathstrut +\mathstrut 2427758859173433876q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.19.b.a \(8\) \(8.215\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(84\) \(0\) \(860880\) \(0\) \(q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots\)