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Properties

Label 385.2.bc
Level $385$
Weight $2$
Character orbit 385.bc
Rep. character $\chi_{385}(32,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{12})\)
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 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176 q - 4 q^{3} - 8 q^{5} + O(q^{10}) \) \( 176 q - 4 q^{3} - 8 q^{5} - 4 q^{11} - 20 q^{12} - 32 q^{15} + 48 q^{16} - 48 q^{20} - 40 q^{22} + 12 q^{23} - 24 q^{25} + 16 q^{26} - 40 q^{27} - 8 q^{31} + 8 q^{33} - 256 q^{36} + 24 q^{37} + 12 q^{38} + 60 q^{42} - 76 q^{45} + 16 q^{47} + 88 q^{48} - 24 q^{53} + 16 q^{55} - 120 q^{56} - 20 q^{58} + 36 q^{60} - 12 q^{66} + 28 q^{67} + 44 q^{70} - 128 q^{71} + 12 q^{75} + 40 q^{77} + 168 q^{78} + 92 q^{80} + 32 q^{81} - 12 q^{82} + 32 q^{86} + 44 q^{88} + 48 q^{91} + 16 q^{92} - 60 q^{93} + 144 q^{97} + O(q^{100}) \)

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.bc.a 385.bc 385.ac $176$ $3.074$ None \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$