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Properties

Label 381.2.c
Level $381$
Weight $2$
Character orbit 381.c
Rep. character $\chi_{381}(380,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $85$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 381 = 3 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 381.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 381 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(85\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(381, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 40 40 0
Eisenstein series 4 4 0

Trace form

\( 40 q - 40 q^{4} + 2 q^{9} + O(q^{10}) \) \( 40 q - 40 q^{4} + 2 q^{9} - 12 q^{13} - 22 q^{15} + 40 q^{16} - 12 q^{18} + 12 q^{19} - 24 q^{21} - 24 q^{22} + 40 q^{25} + 42 q^{30} - 28 q^{31} - 4 q^{34} - 20 q^{36} - 24 q^{37} + 50 q^{42} - 48 q^{49} - 4 q^{52} + 48 q^{60} + 28 q^{61} - 76 q^{64} - 12 q^{69} - 36 q^{70} + 86 q^{72} + 36 q^{73} - 56 q^{76} + 76 q^{79} - 30 q^{81} - 32 q^{82} + 46 q^{84} - 40 q^{87} + 104 q^{88} - 32 q^{94} + 78 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(381, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
381.2.c.a 381.c 381.c $40$ $3.042$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$