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Properties

Label 180.3.c
Level $180$
Weight $3$
Character orbit 180.c
Rep. character $\chi_{180}(91,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $3$
Sturm bound $108$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(108\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 80 20 60
Cusp forms 64 20 44
Eisenstein series 16 0 16

Trace form

\( 20 q - 2 q^{2} - 8 q^{4} + 28 q^{8} + O(q^{10}) \) \( 20 q - 2 q^{2} - 8 q^{4} + 28 q^{8} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 4 q^{16} + 24 q^{17} + 20 q^{20} - 16 q^{22} + 100 q^{25} + 48 q^{26} - 104 q^{28} - 56 q^{29} - 52 q^{32} - 116 q^{34} + 176 q^{37} - 40 q^{38} + 20 q^{40} + 128 q^{41} - 92 q^{44} + 8 q^{46} - 212 q^{49} - 10 q^{50} + 160 q^{52} - 176 q^{53} - 196 q^{56} - 156 q^{58} - 32 q^{61} + 136 q^{62} - 356 q^{64} + 40 q^{65} + 320 q^{68} + 120 q^{70} - 216 q^{73} - 24 q^{74} + 360 q^{76} + 48 q^{77} + 160 q^{80} + 364 q^{82} + 160 q^{85} + 280 q^{86} - 352 q^{88} + 8 q^{89} - 24 q^{92} - 384 q^{94} + 408 q^{97} - 762 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.c.a 180.c 4.b $4$ $4.905$ \(\Q(\zeta_{10})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots\)
180.3.c.b 180.c 4.b $8$ $4.905$ 8.0.85100625.1 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots\)
180.3.c.c 180.c 4.b $8$ $4.905$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{4})q^{4}+\beta _{3}q^{5}+2\beta _{6}q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)