Properties

Label 78.2.k
Level $78$
Weight $2$
Character orbit 78.k
Rep. character $\chi_{78}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $16$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(78, [\chi])\).

Total New Old
Modular forms 72 16 56
Cusp forms 40 16 24
Eisenstein series 32 0 32

Trace form

\( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} - 24q^{10} - 24q^{13} + 8q^{16} - 16q^{19} - 24q^{21} - 8q^{28} + 24q^{30} + 16q^{31} - 24q^{33} + 24q^{34} + 24q^{36} + 16q^{37} + 48q^{39} + 24q^{45} + 24q^{46} + 24q^{49} - 8q^{52} - 24q^{55} - 24q^{57} - 24q^{60} - 24q^{61} - 24q^{63} - 48q^{66} + 32q^{67} - 48q^{69} - 24q^{72} + 56q^{73} - 16q^{76} - 96q^{79} + 24q^{81} - 48q^{82} - 24q^{85} + 48q^{87} - 16q^{91} - 24q^{93} - 24q^{94} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(78, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
78.2.k.a \(16\) \(0.623\) 16.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(8\) \(q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(78, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(78, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)