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Properties

Label 78.4.k
Level $78$
Weight $4$
Character orbit 78.k
Rep. character $\chi_{78}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(78, [\chi])\).

Total New Old
Modular forms 184 56 128
Cusp forms 152 56 96
Eisenstein series 32 0 32

Trace form

\( 56 q - 92 q^{7} + O(q^{10}) \) \( 56 q - 92 q^{7} + 144 q^{10} + 168 q^{13} - 168 q^{15} + 448 q^{16} + 96 q^{18} - 716 q^{19} - 144 q^{21} - 72 q^{27} + 368 q^{28} + 816 q^{30} + 140 q^{31} + 156 q^{33} + 240 q^{34} - 768 q^{36} - 1804 q^{37} - 912 q^{39} - 576 q^{42} - 1092 q^{43} + 492 q^{45} + 48 q^{46} + 2196 q^{49} - 16 q^{52} - 1584 q^{54} + 792 q^{55} + 1020 q^{57} - 1056 q^{58} + 384 q^{60} - 120 q^{61} + 8148 q^{63} - 96 q^{66} + 160 q^{67} + 3516 q^{69} - 192 q^{70} + 576 q^{72} - 4628 q^{73} - 7020 q^{75} - 2864 q^{76} - 5232 q^{78} + 6816 q^{79} - 4224 q^{81} + 864 q^{82} + 1056 q^{84} - 1656 q^{85} - 1008 q^{87} + 8044 q^{91} + 3912 q^{93} + 2256 q^{94} + 4220 q^{97} + 8892 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(78, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
78.4.k.a 78.k 39.k $56$ $4.602$ None 78.4.k.a \(0\) \(0\) \(0\) \(-92\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{4}^{\mathrm{old}}(78, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(78, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)