Properties

Label 59.19.b
Level $59$
Weight $19$
Character orbit 59.b
Rep. character $\chi_{59}(58,\cdot)$
Character field $\Q$
Dimension $89$
Newform subspaces $3$
Sturm bound $95$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 59.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(95\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(59, [\chi])\).

Total New Old
Modular forms 91 91 0
Cusp forms 89 89 0
Eisenstein series 2 2 0

Trace form

\( 89 q - 47870 q^{3} - 11534338 q^{4} - 1461458 q^{5} + 42126406 q^{7} + 10679224559 q^{9} + O(q^{10}) \) \( 89 q - 47870 q^{3} - 11534338 q^{4} - 1461458 q^{5} + 42126406 q^{7} + 10679224559 q^{9} + 13944005596 q^{12} + 195444804060 q^{15} + 1494700729406 q^{16} - 320505008518 q^{17} - 20505417086 q^{19} - 921869660176 q^{20} + 455084712100 q^{21} - 2523101113242 q^{22} + 71373516329967 q^{25} + 4038771265458 q^{26} + 8087608595500 q^{27} + 45682997799418 q^{28} + 13384437130414 q^{29} + 320814281420436 q^{35} - 931742977189938 q^{36} - 1451467766454814 q^{41} - 2110695612420806 q^{45} - 2417237508941748 q^{46} - 1270141731516908 q^{48} + 21844186617126723 q^{49} - 5037084889546004 q^{51} - 251121963530482 q^{53} - 9487072418333676 q^{57} + 36718829609840937 q^{59} - 90187764941042672 q^{60} + 6330618081020380 q^{62} + 12833294777329138 q^{63} - 104394189854096326 q^{64} - 131353435035156400 q^{66} + 87497252943416734 q^{68} + 64801930768366326 q^{71} + 80283634292536118 q^{74} - 331206172164568922 q^{75} - 475525478749367576 q^{76} + 524338818805263656 q^{78} - 247822794733902050 q^{79} + 757098311310332504 q^{80} + 1437950587947411333 q^{81} + 1481351209847938312 q^{84} + 433641754218225164 q^{85} + 1059229941373163878 q^{86} + 2102112542985519988 q^{87} + 1283382060222557034 q^{88} - 2893703721678163368 q^{94} + 1556843544295866892 q^{95} + O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(59, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
59.19.b.a 59.b 59.b $1$ $121.178$ \(\Q\) \(\Q(\sqrt{-59}) \) 59.19.b.a \(0\) \(10810\) \(-1985254\) \(-50982910\) $\mathrm{U}(1)[D_{2}]$ \(q+10810q^{3}+2^{18}q^{4}-1985254q^{5}+\cdots\)
59.19.b.b 59.b 59.b $2$ $121.178$ \(\Q(\sqrt{177}) \) \(\Q(\sqrt{-59}) \) 59.19.b.b \(0\) \(-10810\) \(1985254\) \(50982910\) $\mathrm{U}(1)[D_{2}]$ \(q+(-5405-616\beta )q^{3}+2^{18}q^{4}+(992627+\cdots)q^{5}+\cdots\)
59.19.b.c 59.b 59.b $86$ $121.178$ None 59.19.b.c \(0\) \(-47870\) \(-1461458\) \(42126406\) $\mathrm{SU}(2)[C_{2}]$