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Properties

Label 385.2.bu
Level $385$
Weight $2$
Character orbit 385.bu
Rep. character $\chi_{385}(3,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $704$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.bu (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

Total New Old
Modular forms 832 832 0
Cusp forms 704 704 0
Eisenstein series 128 128 0

Trace form

\( 704 q - 6 q^{2} - 18 q^{3} - 30 q^{5} - 10 q^{7} - 8 q^{8} + O(q^{10}) \) \( 704 q - 6 q^{2} - 18 q^{3} - 30 q^{5} - 10 q^{7} - 8 q^{8} - 72 q^{10} - 24 q^{11} - 72 q^{12} - 84 q^{16} - 18 q^{17} - 2 q^{18} - 64 q^{21} - 48 q^{22} - 32 q^{23} - 26 q^{25} - 12 q^{26} + 80 q^{28} - 10 q^{30} - 36 q^{31} - 48 q^{32} - 180 q^{33} + 8 q^{35} + 176 q^{36} - 10 q^{37} - 18 q^{38} - 18 q^{40} - 16 q^{42} - 104 q^{43} - 144 q^{45} + 68 q^{46} - 6 q^{47} - 88 q^{50} - 44 q^{51} + 30 q^{52} - 26 q^{53} - 136 q^{56} - 112 q^{57} + 58 q^{58} + 14 q^{60} - 36 q^{61} + 112 q^{63} + 40 q^{65} - 48 q^{66} - 64 q^{67} + 78 q^{68} + 68 q^{70} - 144 q^{71} + 14 q^{72} - 78 q^{73} + 174 q^{75} + 80 q^{77} - 312 q^{78} + 210 q^{80} - 72 q^{81} - 90 q^{82} - 24 q^{85} - 52 q^{86} - 60 q^{87} - 26 q^{88} - 28 q^{91} - 8 q^{92} + 122 q^{93} - 24 q^{95} + 72 q^{96} - 344 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
385.2.bu.a 385.bu 385.au $704$ $3.074$ None \(-6\) \(-18\) \(-30\) \(-10\) $\mathrm{SU}(2)[C_{60}]$