Properties

Label 374.2.g
Level $374$
Weight $2$
Character orbit 374.g
Rep. character $\chi_{374}(69,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $64$
Newform subspaces $7$
Sturm bound $108$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 374 = 2 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 374.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 7 \)
Sturm bound: \(108\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 232 64 168
Cusp forms 200 64 136
Eisenstein series 32 0 32

Trace form

\( 64 q + 4 q^{3} - 16 q^{4} + 4 q^{5} + 4 q^{6} + 8 q^{7} - 12 q^{9} + O(q^{10}) \) \( 64 q + 4 q^{3} - 16 q^{4} + 4 q^{5} + 4 q^{6} + 8 q^{7} - 12 q^{9} - 8 q^{10} + 4 q^{11} - 16 q^{12} + 8 q^{13} - 12 q^{14} + 4 q^{15} - 16 q^{16} + 4 q^{17} + 8 q^{18} + 16 q^{19} + 4 q^{20} + 8 q^{21} + 4 q^{22} - 32 q^{23} + 4 q^{24} - 8 q^{25} + 40 q^{27} - 12 q^{28} - 24 q^{29} - 36 q^{30} + 4 q^{31} - 44 q^{33} - 28 q^{35} - 12 q^{36} + 36 q^{37} - 32 q^{38} + 4 q^{39} - 8 q^{40} + 28 q^{41} + 8 q^{42} - 32 q^{43} + 4 q^{44} + 16 q^{45} + 16 q^{46} + 16 q^{47} + 4 q^{48} - 16 q^{49} + 8 q^{50} + 4 q^{51} - 12 q^{52} - 40 q^{54} + 60 q^{55} + 8 q^{56} + 24 q^{57} - 28 q^{58} + 20 q^{59} + 4 q^{60} - 12 q^{61} + 16 q^{62} + 64 q^{63} - 16 q^{64} - 80 q^{65} - 20 q^{66} - 56 q^{67} + 4 q^{68} - 64 q^{69} - 16 q^{70} + 16 q^{71} - 12 q^{72} - 40 q^{73} + 36 q^{74} + 12 q^{75} + 16 q^{76} + 36 q^{77} + 96 q^{78} + 32 q^{79} + 4 q^{80} - 60 q^{81} + 8 q^{82} - 8 q^{83} - 12 q^{84} + 12 q^{85} - 24 q^{86} - 8 q^{87} + 4 q^{88} - 24 q^{90} + 48 q^{91} + 8 q^{92} + 32 q^{93} - 52 q^{94} - 32 q^{95} + 4 q^{96} + 20 q^{97} + 56 q^{98} + 24 q^{99} + O(q^{100}) \)

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.g.a 374.g 11.c $4$ $2.986$ \(\Q(\zeta_{10})\) None \(-1\) \(-4\) \(7\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
374.2.g.b 374.g 11.c $4$ $2.986$ \(\Q(\zeta_{10})\) None \(-1\) \(-2\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
374.2.g.c 374.g 11.c $4$ $2.986$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(-5\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
374.2.g.d 374.g 11.c $8$ $2.986$ 8.0.13140625.1 None \(-2\) \(5\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)
374.2.g.e 374.g 11.c $8$ $2.986$ 8.0.159390625.1 None \(2\) \(3\) \(1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{2}+(1-\beta _{5}-\beta _{6})q^{3}-\beta _{3}q^{4}+\cdots\)
374.2.g.f 374.g 11.c $16$ $2.986$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(5\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{3}-\beta _{6}-\beta _{8})q^{2}+(-\beta _{6}+\cdots)q^{3}+\cdots\)
374.2.g.g 374.g 11.c $20$ $2.986$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(-1\) \(0\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{3}-\beta _{7}-\beta _{9})q^{2}-\beta _{5}q^{3}-\beta _{7}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(374, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)