Properties

Label 4020.2.g
Level $4020$
Weight $2$
Character orbit 4020.g
Rep. character $\chi_{4020}(1609,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $3$
Sturm bound $1632$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4020.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1632\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4020, [\chi])\).

Total New Old
Modular forms 828 64 764
Cusp forms 804 64 740
Eisenstein series 24 0 24

Trace form

\( 64 q - 4 q^{5} - 64 q^{9} + O(q^{10}) \) \( 64 q - 4 q^{5} - 64 q^{9} + 16 q^{11} + 4 q^{15} - 8 q^{21} + 8 q^{25} - 32 q^{29} - 8 q^{31} - 4 q^{35} + 24 q^{41} + 4 q^{45} - 56 q^{49} + 8 q^{55} - 32 q^{59} + 24 q^{61} + 4 q^{65} + 8 q^{75} - 24 q^{79} + 64 q^{81} - 8 q^{85} - 24 q^{89} + 24 q^{91} + 32 q^{95} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4020, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4020.2.g.a 4020.g 5.b $2$ $32.100$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1-2i)q^{5}-q^{9}+2iq^{13}+\cdots\)
4020.2.g.b 4020.g 5.b $24$ $32.100$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
4020.2.g.c 4020.g 5.b $38$ $32.100$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4020, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1340, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2010, [\chi])\)\(^{\oplus 2}\)