Properties

Label 380.2.y
Level $380$
Weight $2$
Character orbit 380.y
Rep. character $\chi_{380}(217,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $40$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 264 40 224
Cusp forms 216 40 176
Eisenstein series 48 0 48

Trace form

\( 40q - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 40q - 2q^{5} - 4q^{7} - 8q^{11} - 18q^{15} + 8q^{17} + 24q^{21} + 16q^{23} + 10q^{25} - 48q^{33} + 4q^{35} + 12q^{41} - 10q^{43} + 76q^{45} + 30q^{47} - 96q^{51} + 18q^{53} + 16q^{55} - 18q^{57} + 8q^{61} - 38q^{63} - 48q^{67} + 36q^{73} - 28q^{77} - 4q^{81} - 44q^{83} + 4q^{85} - 64q^{87} + 72q^{91} - 20q^{93} - 64q^{95} + 6q^{97} + O(q^{100}) \)

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.y.a \(4\) \(3.034\) \(\Q(\zeta_{12})\) None \(0\) \(6\) \(2\) \(-8\) \(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(1+\cdots)q^{5}+\cdots\)
380.2.y.b \(36\) \(3.034\) None \(0\) \(-6\) \(-4\) \(4\)

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

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)