Properties

Label 180.4.i
Level $180$
Weight $4$
Character orbit 180.i
Rep. character $\chi_{180}(61,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $3$
Sturm bound $144$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 180.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(180, [\chi])\).

Total New Old
Modular forms 228 24 204
Cusp forms 204 24 180
Eisenstein series 24 0 24

Trace form

\( 24 q + 2 q^{3} - 10 q^{5} + 12 q^{7} - 28 q^{9} + O(q^{10}) \) \( 24 q + 2 q^{3} - 10 q^{5} + 12 q^{7} - 28 q^{9} - 54 q^{11} - 24 q^{13} - 20 q^{15} + 348 q^{17} - 60 q^{19} + 196 q^{21} - 84 q^{23} - 300 q^{25} - 592 q^{27} - 342 q^{29} - 60 q^{31} + 738 q^{33} + 280 q^{35} + 336 q^{37} - 308 q^{39} - 804 q^{41} - 258 q^{43} - 140 q^{45} - 276 q^{47} - 630 q^{49} + 1518 q^{51} + 3432 q^{53} + 178 q^{57} - 630 q^{59} + 822 q^{61} - 1976 q^{63} - 200 q^{65} - 186 q^{67} - 522 q^{69} - 216 q^{71} - 1500 q^{73} + 50 q^{75} - 96 q^{77} - 888 q^{79} - 412 q^{81} + 228 q^{83} - 360 q^{85} + 2700 q^{87} + 828 q^{89} + 24 q^{91} - 1376 q^{93} + 520 q^{95} - 546 q^{97} + 1512 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.4.i.a 180.i 9.c $2$ $10.620$ \(\Q(\sqrt{-3}) \) None \(0\) \(9\) \(5\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(6-3\zeta_{6})q^{3}+5\zeta_{6}q^{5}+(7-7\zeta_{6})q^{7}+\cdots\)
180.4.i.b 180.i 9.c $8$ $10.620$ 8.0.\(\cdots\).1 None \(0\) \(-12\) \(20\) \(13\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-\beta _{5})q^{3}+5\beta _{2}q^{5}+(5-3\beta _{2}+\cdots)q^{7}+\cdots\)
180.4.i.c 180.i 9.c $14$ $10.620$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(5\) \(-35\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{3}+(-5+5\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)