Properties

Label 304.3.bj
Level $304$
Weight $3$
Character orbit 304.bj
Rep. character $\chi_{304}(13,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $936$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 304.bj (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
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 984 984 0
Cusp forms 936 936 0
Eisenstein series 48 48 0

Trace form

\( 936 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 18 q^{8} + O(q^{10}) \) \( 936 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{10} - 6 q^{11} - 18 q^{12} - 12 q^{13} - 36 q^{14} - 24 q^{15} + 72 q^{16} - 24 q^{17} - 12 q^{19} - 24 q^{20} - 66 q^{21} - 12 q^{22} - 12 q^{24} - 150 q^{26} - 18 q^{27} - 108 q^{28} - 12 q^{29} - 300 q^{30} - 36 q^{31} - 222 q^{32} - 24 q^{33} + 168 q^{34} - 162 q^{35} + 132 q^{36} + 282 q^{38} - 282 q^{40} - 828 q^{42} - 12 q^{43} - 210 q^{44} - 6 q^{45} + 792 q^{46} - 24 q^{47} - 12 q^{48} + 2760 q^{49} - 720 q^{50} - 300 q^{51} - 252 q^{52} - 12 q^{53} - 42 q^{54} - 24 q^{58} - 12 q^{59} + 534 q^{60} - 12 q^{61} - 36 q^{62} - 612 q^{63} - 6 q^{64} - 36 q^{65} - 672 q^{66} - 12 q^{67} - 186 q^{68} + 846 q^{69} + 198 q^{70} + 288 q^{72} + 240 q^{74} - 540 q^{76} - 612 q^{77} + 684 q^{78} - 24 q^{79} + 48 q^{80} - 24 q^{81} - 192 q^{82} - 6 q^{83} - 18 q^{84} + 948 q^{85} - 12 q^{86} - 18 q^{88} - 552 q^{90} - 306 q^{91} - 12 q^{92} - 66 q^{93} - 24 q^{95} + 1404 q^{96} - 24 q^{97} + 264 q^{98} - 498 q^{99} + O(q^{100}) \)

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.bj.a 304.bj 304.aj $936$ $8.283$ None \(-12\) \(-12\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{36}]$