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Properties

Label 798.2.bu
Level $798$
Weight $2$
Character orbit 798.bu
Rep. character $\chi_{798}(53,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $324$
Newform subspaces $2$
Sturm bound $320$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.bu (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(320\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(798, [\chi])\).

Total New Old
Modular forms 1008 324 684
Cusp forms 912 324 588
Eisenstein series 96 0 96

Trace form

\( 324 q + 30 q^{13} + 30 q^{15} - 36 q^{18} + 18 q^{19} - 12 q^{22} - 12 q^{25} + 18 q^{28} + 12 q^{34} + 36 q^{37} - 18 q^{39} - 18 q^{43} - 18 q^{45} - 96 q^{49} - 30 q^{52} - 36 q^{57} + 24 q^{60} + 90 q^{61}+ \cdots - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(798, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
798.2.bu.a 798.bu 399.ar $162$ $6.372$ None 798.2.bu.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
798.2.bu.b 798.bu 399.ar $162$ $6.372$ None 798.2.bu.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(798, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(798, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)