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Properties

Label 810.2.p
Level $810$
Weight $2$
Character orbit 810.p
Rep. character $\chi_{810}(19,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.p (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(324\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(810, [\chi])\).

Total New Old
Modular forms 1044 108 936
Cusp forms 900 108 792
Eisenstein series 144 0 144

Trace form

\( 108 q - 6 q^{5} + O(q^{10}) \) \( 108 q - 6 q^{5} + 12 q^{11} - 6 q^{14} - 12 q^{20} - 18 q^{25} + 72 q^{26} - 6 q^{29} + 36 q^{31} - 18 q^{35} + 12 q^{41} + 12 q^{44} + 18 q^{49} + 12 q^{50} + 6 q^{56} + 84 q^{59} - 18 q^{61} + 54 q^{64} + 6 q^{65} + 48 q^{74} - 72 q^{79} + 36 q^{86} + 132 q^{89} - 36 q^{94} + 18 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(810, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
810.2.p.a 810.p 135.p $108$ $6.468$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(810, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(810, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)