↑

Properties

Label 351.2.w
Level $351$
Weight $2$
Character orbit 351.w
Rep. character $\chi_{351}(40,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $216$
Newform subspaces $3$
Sturm bound $84$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 351.w (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 3 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(351, [\chi])\).

Total New Old
Modular forms 264 216 48
Cusp forms 240 216 24
Eisenstein series 24 0 24

Trace form

\( 216 q - 6 q^{5} - 12 q^{6} - 18 q^{8} + O(q^{10}) \) \( 216 q - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{11} - 18 q^{12} - 42 q^{14} - 6 q^{15} - 30 q^{18} + 6 q^{20} + 36 q^{21} - 18 q^{22} + 36 q^{23} - 30 q^{24} - 18 q^{25} + 36 q^{26} - 30 q^{27} - 36 q^{29} + 36 q^{30} - 18 q^{31} - 60 q^{32} - 12 q^{33} - 18 q^{34} + 18 q^{35} - 18 q^{36} - 18 q^{38} - 18 q^{41} - 48 q^{42} - 18 q^{43} - 60 q^{44} - 36 q^{45} - 24 q^{47} + 72 q^{48} - 36 q^{49} - 48 q^{50} + 66 q^{51} + 168 q^{54} + 72 q^{56} - 60 q^{57} + 48 q^{59} - 132 q^{60} - 36 q^{61} + 66 q^{62} - 60 q^{63} - 108 q^{64} - 90 q^{66} + 18 q^{67} + 72 q^{68} - 6 q^{69} + 72 q^{70} - 60 q^{71} - 60 q^{72} + 6 q^{74} - 42 q^{75} + 108 q^{76} - 18 q^{77} - 12 q^{80} + 24 q^{81} - 12 q^{83} + 102 q^{84} - 102 q^{86} - 42 q^{87} + 108 q^{88} - 24 q^{89} + 18 q^{90} - 126 q^{92} + 96 q^{93} + 72 q^{94} + 36 q^{95} + 84 q^{96} - 18 q^{97} - 54 q^{98} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(351, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
351.2.w.a 351.w 27.e $6$ $2.803$ \(\Q(\zeta_{18})\) None \(3\) \(0\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots\)
351.2.w.b 351.w 27.e $102$ $2.803$ None \(-3\) \(0\) \(-9\) \(6\) $\mathrm{SU}(2)[C_{9}]$
351.2.w.c 351.w 27.e $108$ $2.803$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(351, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(351, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)