Properties

Label 78.2.b
Level $78$
Weight $2$
Character orbit 78.b
Rep. character $\chi_{78}(25,\cdot)$
Character field $\Q$
Dimension $2$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
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 18 2 16
Cusp forms 10 2 8
Eisenstein series 8 0 8

Trace form

\( 2q + 2q^{3} - 2q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{4} + 2q^{9} - 4q^{10} - 2q^{12} - 6q^{13} + 4q^{14} + 2q^{16} - 4q^{17} + 8q^{23} + 2q^{25} + 4q^{26} + 2q^{27} - 20q^{29} - 4q^{30} + 8q^{35} - 2q^{36} + 12q^{38} - 6q^{39} + 4q^{40} + 4q^{42} + 8q^{43} + 2q^{48} + 6q^{49} - 4q^{51} + 6q^{52} - 12q^{53} - 4q^{56} + 4q^{61} - 20q^{62} - 2q^{64} + 8q^{65} + 4q^{68} + 8q^{69} - 16q^{74} + 2q^{75} + 4q^{78} + 2q^{81} - 20q^{82} - 20q^{87} - 4q^{90} - 8q^{91} - 8q^{92} + 24q^{94} + 24q^{95} + O(q^{100}) \)

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.b.a \(2\) \(0.623\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(78, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)