Properties

Label 74.2.e
Level $74$
Weight $2$
Character orbit 74.e
Rep. character $\chi_{74}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $19$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(19\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(74, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 16 8 8
Eisenstein series 8 0 8

Trace form

\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{7} - 4 q^{9} + 4 q^{12} - 12 q^{13} - 4 q^{16} - 4 q^{21} - 8 q^{25} - 24 q^{26} + 32 q^{27} + 4 q^{28} - 12 q^{30} + 12 q^{33} + 12 q^{34} + 36 q^{35} - 8 q^{36} - 4 q^{37} - 24 q^{39} + 36 q^{42} + 12 q^{46} + 24 q^{47} + 8 q^{48} - 12 q^{49} - 12 q^{52} - 36 q^{55} - 36 q^{57} - 12 q^{58} + 36 q^{61} - 12 q^{62} + 8 q^{63} - 8 q^{64} - 12 q^{65} + 8 q^{67} - 12 q^{71} + 8 q^{73} - 24 q^{74} + 16 q^{75} - 36 q^{77} + 24 q^{78} - 12 q^{79} - 4 q^{81} - 12 q^{83} - 8 q^{84} + 24 q^{85} + 24 q^{86} - 72 q^{87} + 36 q^{89} - 24 q^{90} - 24 q^{91} - 12 q^{93} + 36 q^{94} - 12 q^{95} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.2.e.a 74.e 37.e $4$ $0.591$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
74.2.e.b 74.e 37.e $4$ $0.591$ \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(6\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)