↑

Properties

Label 180.2.q
Level $180$
Weight $2$
Character orbit 180.q
Rep. character $\chi_{180}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 180.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(180, [\chi])\).

Total New Old
Modular forms 80 48 32
Cusp forms 64 48 16
Eisenstein series 16 0 16

Trace form

\( 48 q + 6 q^{6} + 4 q^{9} + O(q^{10}) \) \( 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42} - 8 q^{45} - 12 q^{46} - 12 q^{48} + 24 q^{49} - 18 q^{52} - 32 q^{54} - 42 q^{56} - 12 q^{57} - 18 q^{58} + 14 q^{60} - 48 q^{64} + 16 q^{66} + 48 q^{68} + 36 q^{69} + 60 q^{72} - 24 q^{73} + 84 q^{74} + 6 q^{76} + 48 q^{77} + 38 q^{78} - 36 q^{82} + 50 q^{84} - 54 q^{86} - 18 q^{90} + 60 q^{92} - 32 q^{93} + 18 q^{94} - 18 q^{96} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.2.q.a 180.q 36.h $48$ $1.437$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)