Properties

Label 380.2.k
Level $380$
Weight $2$
Character orbit 380.k
Rep. character $\chi_{380}(267,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $108$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 128 108 20
Cusp forms 112 108 4
Eisenstein series 16 0 16

Trace form

\( 108q + O(q^{10}) \) \( 108q - 16q^{10} - 16q^{12} - 4q^{13} + 16q^{16} - 20q^{17} - 16q^{21} - 16q^{22} - 20q^{25} - 32q^{28} - 24q^{30} - 40q^{32} + 16q^{33} - 16q^{36} + 20q^{37} + 24q^{40} + 20q^{45} - 48q^{46} - 20q^{48} + 4q^{50} + 20q^{52} - 44q^{53} - 8q^{56} - 32q^{58} - 20q^{60} + 24q^{62} + 20q^{65} + 72q^{66} + 8q^{68} + 76q^{70} + 100q^{72} + 36q^{73} + 24q^{77} + 24q^{78} - 96q^{80} - 28q^{81} - 24q^{82} + 4q^{85} + 32q^{86} - 20q^{88} - 16q^{90} - 40q^{92} + 48q^{93} - 40q^{96} - 60q^{97} - 64q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
380.2.k.a \(2\) \(3.034\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-2\) \(-4\) \(-4\) \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
380.2.k.b \(2\) \(3.034\) \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(-4\) \(4\) \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
380.2.k.c \(52\) \(3.034\) None \(-2\) \(-2\) \(4\) \(-4\)
380.2.k.d \(52\) \(3.034\) None \(2\) \(2\) \(4\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)