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Properties

Label 532.2.u
Level $532$
Weight $2$
Character orbit 532.u
Rep. character $\chi_{532}(83,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Newform subspaces $2$
Sturm bound $160$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 532.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 532 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(532, [\chi])\).

Total New Old
Modular forms 168 168 0
Cusp forms 152 152 0
Eisenstein series 16 16 0

Trace form

\( 152 q - 2 q^{2} - 2 q^{4} - 20 q^{8} - 72 q^{9} - 2 q^{14} - 2 q^{16} + 12 q^{18} - 4 q^{21} + 2 q^{22} + 56 q^{25} + 10 q^{28} - 4 q^{29} - 24 q^{30} - 12 q^{32} + 28 q^{36} - 32 q^{37} + 4 q^{42} + 28 q^{44}+ \cdots - 66 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(532, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
532.2.u.a 532.u 532.u $16$ $4.248$ 16.0.\(\cdots\).16 None 532.2.u.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{5}+\beta _{7})q^{2}+(\beta _{1}-\beta _{13})q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\)
532.2.u.b 532.u 532.u $136$ $4.248$ None 532.2.u.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$