↑

Properties

Label 931.2.ca
Level $931$
Weight $2$
Character orbit 931.ca
Rep. character $\chi_{931}(4,\cdot)$
Character field $\Q(\zeta_{63})$
Dimension $3276$
Newform subspaces $1$
Sturm bound $186$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.ca (of order \(63\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 931 \)
Character field: \(\Q(\zeta_{63})\)
Newform subspaces: \( 1 \)
Sturm bound: \(186\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

Total New Old
Modular forms 3420 3420 0
Cusp forms 3276 3276 0
Eisenstein series 144 144 0

Trace form

\( 3276 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} - 30 q^{6} - 12 q^{7} - 15 q^{8} - 39 q^{9} + O(q^{10}) \) \( 3276 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} - 30 q^{6} - 12 q^{7} - 15 q^{8} - 39 q^{9} - 57 q^{10} + 33 q^{12} - 30 q^{13} - 39 q^{14} - 21 q^{15} - 51 q^{16} - 42 q^{17} - 36 q^{18} - 27 q^{19} - 60 q^{21} - 18 q^{22} - 39 q^{23} - 6 q^{24} - 39 q^{25} - 45 q^{26} - 51 q^{27} - 87 q^{28} - 42 q^{29} + 18 q^{30} + 234 q^{31} + 78 q^{32} - 3 q^{33} - 18 q^{34} - 99 q^{35} - 51 q^{36} - 90 q^{37} + 30 q^{38} - 60 q^{39} - 99 q^{40} - 12 q^{41} - 45 q^{42} - 54 q^{43} + 132 q^{44} + 87 q^{45} + 15 q^{46} - 21 q^{47} - 63 q^{48} - 69 q^{50} - 39 q^{51} - 201 q^{52} - 21 q^{53} - 72 q^{54} - 15 q^{55} - 96 q^{56} - 36 q^{57} - 78 q^{58} - 48 q^{59} - 12 q^{60} + 150 q^{61} + 69 q^{62} + 276 q^{63} + 195 q^{64} - 42 q^{65} + 153 q^{66} - 27 q^{67} + 36 q^{68} - 63 q^{69} - 57 q^{70} + 15 q^{71} + 351 q^{72} + 36 q^{73} - 129 q^{74} - 141 q^{75} - 84 q^{76} - 102 q^{77} - 105 q^{78} + 42 q^{79} - 18 q^{80} - 78 q^{81} - 54 q^{82} - 3 q^{83} - 222 q^{84} - 342 q^{85} - 258 q^{86} - 39 q^{87} + 24 q^{88} - 165 q^{89} + 174 q^{90} + 90 q^{91} - 24 q^{92} + 264 q^{93} - 366 q^{94} - 111 q^{95} + 561 q^{96} - 87 q^{97} - 48 q^{98} - 144 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
931.2.ca.a 931.ca 931.ba $3276$ $7.434$ None \(-39\) \(-39\) \(-39\) \(-12\) $\mathrm{SU}(2)[C_{63}]$