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Properties

Label 820.2.bw
Level $820$
Weight $2$
Character orbit 820.bw
Rep. character $\chi_{820}(11,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1344$
Newform subspaces $2$
Sturm bound $252$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 820.bw (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{40})\)
Newform subspaces: \( 2 \)
Sturm bound: \(252\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(820, [\chi])\).

Total New Old
Modular forms 2080 1344 736
Cusp forms 1952 1344 608
Eisenstein series 128 0 128

Trace form

\( 1344 q + 24 q^{6} + 16 q^{9} - 24 q^{12} - 16 q^{17} + 48 q^{22} - 48 q^{24} - 40 q^{32} + 80 q^{33} + 40 q^{34} - 24 q^{36} - 120 q^{38} + 80 q^{48} - 16 q^{49} - 88 q^{52} - 128 q^{54} + 136 q^{56} - 56 q^{58}+ \cdots - 232 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(820, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
820.2.bw.a 820.bw 164.o $672$ $6.548$ None 820.2.bw.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{40}]$
820.2.bw.b 820.bw 164.o $672$ $6.548$ None 820.2.bw.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{40}]$

Decomposition of \(S_{2}^{\mathrm{old}}(820, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(820, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 2}\)