↑

Properties

Label 216.3.e
Level $216$
Weight $3$
Character orbit 216.e
Rep. character $\chi_{216}(161,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $108$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(108\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(216, [\chi])\).

Total New Old
Modular forms 84 8 76
Cusp forms 60 8 52
Eisenstein series 24 0 24

Trace form

\( 8 q - 12 q^{7} + O(q^{10}) \) \( 8 q - 12 q^{7} - 28 q^{13} + 16 q^{19} + 52 q^{25} + 76 q^{31} - 84 q^{37} - 136 q^{43} - 32 q^{49} - 4 q^{55} + 284 q^{61} + 88 q^{67} - 64 q^{73} - 280 q^{79} - 344 q^{85} + 456 q^{91} + 184 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.3.e.a 216.e 3.b $2$ $5.886$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}-3q^{7}+7\beta q^{11}+7q^{13}+5\beta q^{17}+\cdots\)
216.3.e.b 216.e 3.b $2$ $5.886$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+3q^{7}+\beta q^{11}-17q^{13}+5\beta q^{17}+\cdots\)
216.3.e.c 216.e 3.b $4$ $5.886$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{8}+\zeta_{8}^{2})q^{5}+(-3+\zeta_{8}^{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)