↑

Properties

Label 828.2.be
Level $828$
Weight $2$
Character orbit 828.be
Rep. character $\chi_{828}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $480$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 828.be (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).

Total New Old
Modular forms 3000 480 2520
Cusp forms 2760 480 2280
Eisenstein series 240 0 240

Trace form

\( 480 q + 2 q^{3} - 6 q^{9} + O(q^{10}) \) \( 480 q + 2 q^{3} - 6 q^{9} + 22 q^{15} - 33 q^{21} - 21 q^{23} + 30 q^{25} - 31 q^{27} + 6 q^{29} + 6 q^{31} + 22 q^{33} + 18 q^{39} + 12 q^{41} + 48 q^{47} - 78 q^{49} + 12 q^{55} + 33 q^{57} + 36 q^{59} + 55 q^{63} + 231 q^{65} + 44 q^{69} + 35 q^{75} - 30 q^{77} - 18 q^{81} + 99 q^{83} + 70 q^{87} - 38 q^{93} + 84 q^{95} + 33 q^{97} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
828.2.be.a 828.be 207.o $480$ $6.612$ None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{66}]$

Decomposition of \(S_{2}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)