Properties

Label 588.2.n
Level $588$
Weight $2$
Character orbit 588.n
Rep. character $\chi_{588}(263,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Newform subspaces $8$
Sturm bound $224$
Trace bound $6$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(224\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(19\), \(67\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).

Total New Old
Modular forms 256 176 80
Cusp forms 192 144 48
Eisenstein series 64 32 32

Trace form

\( 144 q + 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 144 q + 2 q^{4} + 2 q^{9} + 10 q^{10} + 12 q^{12} + 24 q^{13} + 18 q^{16} - 2 q^{18} - 68 q^{22} + 14 q^{24} + 48 q^{25} + 6 q^{30} - 10 q^{33} + 8 q^{34} - 76 q^{36} + 8 q^{37} - 34 q^{40} + 18 q^{45} - 8 q^{46} - 8 q^{48} - 16 q^{52} - 38 q^{54} - 36 q^{57} - 34 q^{58} - 54 q^{60} - 4 q^{61} + 68 q^{64} - 30 q^{66} - 36 q^{69} - 44 q^{72} + 24 q^{76} + 48 q^{78} - 34 q^{81} + 68 q^{82} - 24 q^{85} + 38 q^{88} + 40 q^{90} - 30 q^{93} + 24 q^{94} + 62 q^{96} - 72 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.2.n.a 588.n 84.n $4$ $4.695$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-21}) \) \(0\) \(-6\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
588.2.n.b 588.n 84.n $4$ $4.695$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-21}) \) \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.n.c 588.n 84.n $16$ $4.695$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots\)
588.2.n.d 588.n 84.n $24$ $4.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
588.2.n.e 588.n 84.n $24$ $4.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
588.2.n.f 588.n 84.n $24$ $4.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
588.2.n.g 588.n 84.n $24$ $4.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
588.2.n.h 588.n 84.n $24$ $4.695$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)