↑

Properties

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

Related objects

Downloads

Learn more

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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4.19.b.a 4.b 4.b $8$ $8.215$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4.19.b.a \(84\) \(0\) \(860880\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots\)