Properties

Label 180.3.g
Level $180$
Weight $3$
Character orbit 180.g
Rep. character $\chi_{180}(161,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(180, [\chi])\).

Total New Old
Modular forms 84 4 80
Cusp forms 60 4 56
Eisenstein series 24 0 24

Trace form

\( 4 q - 16 q^{7} + O(q^{10}) \) \( 4 q - 16 q^{7} + 8 q^{13} + 32 q^{19} - 20 q^{25} + 8 q^{31} - 136 q^{37} + 80 q^{43} + 228 q^{49} - 120 q^{55} - 40 q^{61} - 304 q^{67} + 152 q^{73} + 200 q^{79} + 328 q^{91} - 424 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.3.g.a 180.g 3.b $4$ $4.905$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-\beta _{1}-6\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)