Properties

Label 810.2.v
Level $810$
Weight $2$
Character orbit 810.v
Rep. character $\chi_{810}(49,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $972$
Newform subspaces $1$
Sturm bound $324$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.v (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 405 \)
Character field: \(\Q(\zeta_{54})\)
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 2988 972 2016
Cusp forms 2844 972 1872
Eisenstein series 144 0 144

Trace form

\( 972 q + O(q^{10}) \) \( 972 q - 18 q^{20} + 108 q^{21} + 108 q^{26} - 54 q^{30} - 54 q^{35} + 36 q^{36} - 18 q^{41} + 54 q^{45} - 108 q^{51} + 108 q^{59} + 54 q^{65} - 126 q^{69} - 144 q^{74} + 108 q^{79} - 36 q^{84} - 360 q^{89} + 54 q^{94} + 54 q^{95} - 72 q^{99} + O(q^{100}) \)

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.v.a 810.v 405.t $972$ $6.468$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{54}]$

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

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