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Properties

Label 588.2.t
Level $588$
Weight $2$
Character orbit 588.t
Rep. character $\chi_{588}(41,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $108$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 708 108 600
Cusp forms 636 108 528
Eisenstein series 72 0 72

Trace form

\( 108 q - 4 q^{7} - 10 q^{9} - 6 q^{15} + 6 q^{21} - 10 q^{25} - 21 q^{27} + 12 q^{37} - 22 q^{39} + 20 q^{43} - 91 q^{45} + 26 q^{49} - 6 q^{51} + 154 q^{55} - 41 q^{57} + 70 q^{61} + 12 q^{63} + 36 q^{67}+ \cdots + 94 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
588.2.t.a 588.t 147.k $12$ $4.695$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) 588.2.t.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{14}]$ \(q+\beta_{11} q^{3}+(-\beta_{10}-2\beta_{5})q^{7}-3\beta_1 q^{9}+\cdots\)
588.2.t.b 588.t 147.k $96$ $4.695$ None 588.2.t.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$

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

\( S_{2}^{\mathrm{old}}(588, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)