↑

Properties

Label 304.3.j
Level $304$
Weight $3$
Character orbit 304.j
Rep. character $\chi_{304}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $156$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 304.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(304, [\chi])\).

Total New Old
Modular forms 164 164 0
Cusp forms 156 156 0
Eisenstein series 8 8 0

Trace form

\( 156 q - 4 q^{4} - 4 q^{5} - 4 q^{6} + O(q^{10}) \) \( 156 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{11} - 60 q^{16} - 8 q^{17} + 30 q^{19} + 80 q^{20} + 52 q^{24} + 144 q^{26} - 184 q^{30} + 192 q^{35} - 36 q^{36} - 184 q^{38} - 60 q^{42} - 4 q^{43} - 12 q^{44} + 132 q^{45} - 8 q^{47} - 932 q^{49} + 160 q^{54} + 80 q^{58} - 68 q^{61} - 372 q^{62} + 384 q^{63} + 128 q^{64} + 100 q^{66} - 576 q^{68} + 88 q^{74} + 580 q^{76} + 192 q^{77} - 80 q^{80} - 1124 q^{81} - 100 q^{82} + 156 q^{83} + 216 q^{85} - 72 q^{92} + 32 q^{93} + 380 q^{95} + 1200 q^{96} + 484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.3.j.a 304.j 304.j $156$ $8.283$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$