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Properties

Label 381.2.s
Level $381$
Weight $2$
Character orbit 381.s
Rep. character $\chi_{381}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $480$
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.s (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 381 \)
Character field: \(\Q(\zeta_{42})\)
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 528 528 0
Cusp forms 480 480 0
Eisenstein series 48 48 0

Trace form

\( 480 q - 11 q^{3} + 52 q^{4} - 29 q^{6} + 12 q^{7} - 23 q^{9} + O(q^{10}) \) \( 480 q - 11 q^{3} + 52 q^{4} - 29 q^{6} + 12 q^{7} - 23 q^{9} - 28 q^{10} + q^{12} - 16 q^{13} + 6 q^{15} - 116 q^{16} + 4 q^{18} - 32 q^{19} - 77 q^{21} - 32 q^{22} - 15 q^{24} - 72 q^{25} - 14 q^{27} + 132 q^{28} - 19 q^{30} - 14 q^{31} + 7 q^{33} + 14 q^{34} + 31 q^{36} + 4 q^{37} - 47 q^{39} - 84 q^{40} - 30 q^{42} - 60 q^{43} + 40 q^{45} - 66 q^{46} - 18 q^{48} - 88 q^{49} - 7 q^{51} - 22 q^{52} + 14 q^{54} - 52 q^{55} - 86 q^{57} - 8 q^{58} - 74 q^{60} - 6 q^{61} - 98 q^{63} - 80 q^{64} - 42 q^{66} + 10 q^{67} - 13 q^{69} + 18 q^{70} - 42 q^{72} - 64 q^{73} + 222 q^{75} - 208 q^{76} - 89 q^{78} - 164 q^{79} - 79 q^{81} - 80 q^{82} + 114 q^{84} + 22 q^{85} - 54 q^{87} + 522 q^{88} + 9 q^{90} + 2 q^{91} + 106 q^{93} + 192 q^{94} - 259 q^{96} - 170 q^{97} - 10 q^{99} + O(q^{100}) \)

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.s.a 381.s 381.s $480$ $3.042$ None \(0\) \(-11\) \(0\) \(12\) $\mathrm{SU}(2)[C_{42}]$