↑

Properties

Label 531.2.i
Level $531$
Weight $2$
Character orbit 531.i
Rep. character $\chi_{531}(19,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $672$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 531.i (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(531, [\chi])\).

Total New Old
Modular forms 1792 728 1064
Cusp forms 1568 672 896
Eisenstein series 224 56 168

Trace form

\( 672 q + 26 q^{2} - 50 q^{4} + 25 q^{5} - 31 q^{7} + 20 q^{8} + O(q^{10}) \) \( 672 q + 26 q^{2} - 50 q^{4} + 25 q^{5} - 31 q^{7} + 20 q^{8} - 27 q^{10} + 27 q^{11} - 23 q^{13} + 31 q^{14} - 44 q^{16} + 26 q^{17} - 15 q^{19} + 21 q^{20} - 25 q^{22} + 13 q^{23} - 49 q^{25} + 39 q^{26} - 27 q^{28} + 41 q^{29} - 21 q^{31} + 8 q^{32} - 37 q^{34} + 36 q^{35} - 25 q^{37} + 61 q^{38} - 25 q^{40} + 21 q^{41} - 29 q^{43} + 41 q^{44} - 95 q^{46} - 16 q^{47} - 107 q^{49} - 116 q^{50} - 123 q^{52} - 29 q^{53} - 120 q^{55} - 221 q^{56} - 140 q^{58} - 23 q^{59} - 79 q^{61} - 5 q^{62} - 252 q^{64} - 66 q^{65} - 59 q^{67} - 99 q^{68} - 129 q^{70} + 10 q^{71} - 56 q^{73} - 47 q^{74} + q^{76} + 43 q^{77} - 23 q^{79} + 45 q^{80} + q^{82} + 35 q^{83} - 49 q^{85} + 25 q^{86} - 65 q^{88} + 9 q^{89} + 5 q^{91} + 29 q^{92} + 7 q^{94} + 43 q^{95} - 53 q^{97} - 17 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(531, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
531.2.i.a 531.i 59.c $112$ $4.240$ None \(26\) \(0\) \(25\) \(-23\) $\mathrm{SU}(2)[C_{29}]$
531.2.i.b 531.i 59.c $140$ $4.240$ None \(-1\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{29}]$
531.2.i.c 531.i 59.c $140$ $4.240$ None \(1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{29}]$
531.2.i.d 531.i 59.c $280$ $4.240$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{29}]$

Decomposition of \(S_{2}^{\mathrm{old}}(531, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(531, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)