↑

Properties

Label 555.2.bc
Level $555$
Weight $2$
Character orbit 555.bc
Rep. character $\chi_{555}(16,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $156$
Newform subspaces $5$
Sturm bound $152$
Trace bound $6$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.bc (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 5 \)
Sturm bound: \(152\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(555, [\chi])\).

Total New Old
Modular forms 480 156 324
Cusp forms 432 156 276
Eisenstein series 48 0 48

Trace form

\( 156 q + 12 q^{2} + 12 q^{4} + 6 q^{7} - 12 q^{8} + O(q^{10}) \) \( 156 q + 12 q^{2} + 12 q^{4} + 6 q^{7} - 12 q^{8} + 12 q^{10} - 36 q^{13} - 12 q^{14} + 36 q^{16} + 12 q^{18} - 12 q^{19} + 18 q^{21} + 12 q^{22} + 6 q^{27} - 12 q^{28} - 12 q^{29} + 48 q^{31} - 204 q^{32} - 24 q^{33} + 24 q^{34} + 12 q^{35} + 168 q^{36} - 102 q^{37} - 48 q^{38} - 42 q^{39} - 48 q^{42} - 24 q^{44} - 12 q^{46} - 12 q^{47} + 24 q^{48} + 18 q^{49} + 12 q^{50} + 96 q^{52} + 48 q^{53} + 12 q^{55} + 24 q^{56} + 60 q^{58} - 12 q^{59} + 24 q^{61} - 168 q^{62} + 24 q^{63} - 132 q^{64} + 36 q^{65} - 66 q^{67} - 192 q^{68} + 36 q^{69} - 24 q^{71} + 24 q^{72} - 144 q^{73} - 60 q^{74} - 12 q^{75} + 24 q^{76} - 12 q^{77} + 60 q^{78} - 18 q^{79} - 84 q^{82} - 12 q^{83} + 24 q^{85} + 132 q^{86} + 12 q^{87} - 12 q^{88} + 96 q^{89} + 6 q^{91} + 180 q^{92} - 18 q^{93} - 144 q^{94} - 24 q^{97} + 108 q^{98} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(555, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
555.2.bc.a 555.bc 37.f $6$ $4.432$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}^{2}q^{3}+2\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
555.2.bc.b 555.bc 37.f $36$ $4.432$ None \(3\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$
555.2.bc.c 555.bc 37.f $36$ $4.432$ None \(3\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
555.2.bc.d 555.bc 37.f $36$ $4.432$ None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
555.2.bc.e 555.bc 37.f $42$ $4.432$ None \(3\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(555, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(555, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)