↑

Properties

Label 480.2.cc
Level $480$
Weight $2$
Character orbit 480.cc
Rep. character $\chi_{480}(163,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $192$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 480.cc (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 160 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(480, [\chi])\).

Total New Old
Modular forms 400 192 208
Cusp forms 368 192 176
Eisenstein series 32 0 32

Trace form

\( 192 q - 24 q^{8} + O(q^{10}) \) \( 192 q - 24 q^{8} - 24 q^{10} + 16 q^{12} + 16 q^{19} + 16 q^{22} - 40 q^{32} + 8 q^{34} + 48 q^{35} - 56 q^{38} - 40 q^{40} + 40 q^{42} - 32 q^{43} + 32 q^{44} + 32 q^{48} + 192 q^{49} - 16 q^{51} - 88 q^{52} - 32 q^{55} - 96 q^{56} + 32 q^{58} + 32 q^{61} + 72 q^{62} + 96 q^{64} - 48 q^{66} + 48 q^{67} - 56 q^{68} - 72 q^{70} - 64 q^{71} - 72 q^{76} - 48 q^{78} - 168 q^{80} - 120 q^{82} - 80 q^{83} - 64 q^{86} - 72 q^{88} + 16 q^{90} - 72 q^{92} - 64 q^{94} - 112 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(480, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
480.2.cc.a 480.cc 160.aa $192$ $3.833$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)