Properties

Label 374.2.o
Level $374$
Weight $2$
Character orbit 374.o
Rep. character $\chi_{374}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $144$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 374 = 2 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 374.o (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 187 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(374, [\chi])\).

Total New Old
Modular forms 464 144 320
Cusp forms 400 144 256
Eisenstein series 64 0 64

Trace form

\( 144 q + 4 q^{3} + 36 q^{4} - 8 q^{5} - 6 q^{6} - 12 q^{7} + O(q^{10}) \) \( 144 q + 4 q^{3} + 36 q^{4} - 8 q^{5} - 6 q^{6} - 12 q^{7} - 14 q^{11} - 4 q^{12} + 48 q^{13} - 8 q^{14} - 36 q^{16} + 12 q^{17} - 28 q^{18} + 8 q^{20} - 48 q^{21} + 10 q^{22} - 24 q^{23} + 6 q^{24} - 14 q^{27} - 8 q^{28} + 4 q^{29} + 16 q^{30} + 16 q^{31} - 8 q^{33} - 36 q^{34} - 48 q^{37} - 8 q^{38} - 56 q^{39} + 48 q^{41} - 36 q^{44} + 40 q^{45} - 40 q^{46} + 8 q^{47} + 4 q^{48} - 28 q^{50} + 4 q^{51} + 32 q^{52} - 16 q^{54} + 16 q^{55} + 8 q^{56} + 66 q^{57} - 8 q^{58} - 28 q^{61} - 12 q^{62} - 24 q^{63} + 36 q^{64} - 48 q^{65} + 80 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 12 q^{72} - 12 q^{73} + 26 q^{75} + 64 q^{78} - 52 q^{79} + 12 q^{80} - 140 q^{81} + 42 q^{82} + 8 q^{84} - 28 q^{85} + 16 q^{86} - 30 q^{88} - 16 q^{89} + 88 q^{91} - 36 q^{92} - 52 q^{95} + 4 q^{96} - 42 q^{97} - 128 q^{98} + 138 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(374, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
374.2.o.a 374.o 187.p $64$ $2.986$ None \(0\) \(0\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
374.2.o.b 374.o 187.p $80$ $2.986$ None \(0\) \(4\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(374, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(374, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)