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Properties

Label 368.2.j
Level $368$
Weight $2$
Character orbit 368.j
Rep. character $\chi_{368}(93,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $5$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 368.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

Total New Old
Modular forms 100 88 12
Cusp forms 92 88 4
Eisenstein series 8 0 8

Trace form

\( 88 q - 6 q^{6} - 12 q^{8} + O(q^{10}) \) \( 88 q - 6 q^{6} - 12 q^{8} - 12 q^{10} + 10 q^{12} + 16 q^{14} - 20 q^{18} - 12 q^{20} - 8 q^{22} - 12 q^{24} - 32 q^{26} + 12 q^{27} - 24 q^{28} - 4 q^{30} + 24 q^{31} + 20 q^{34} + 24 q^{35} + 46 q^{36} + 20 q^{42} - 32 q^{43} - 40 q^{47} - 88 q^{49} + 12 q^{50} - 40 q^{51} + 8 q^{52} - 12 q^{54} - 28 q^{56} - 10 q^{58} + 20 q^{59} - 20 q^{60} - 38 q^{62} + 42 q^{64} - 16 q^{65} + 20 q^{66} - 24 q^{67} + 28 q^{68} - 28 q^{70} + 78 q^{72} + 24 q^{74} - 24 q^{75} - 60 q^{76} + 58 q^{78} - 60 q^{80} - 88 q^{81} - 58 q^{82} + 40 q^{83} + 88 q^{84} - 56 q^{86} + 68 q^{90} + 16 q^{91} - 24 q^{93} + 52 q^{94} + 16 q^{95} - 80 q^{96} - 4 q^{98} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
368.2.j.a 368.j 16.e $2$ $2.938$ \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(1-i)q^{3}-2iq^{4}-2iq^{6}+\cdots\)
368.2.j.b 368.j 16.e $4$ $2.938$ \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
368.2.j.c 368.j 16.e $12$ $2.938$ 12.0.\(\cdots\).1 None \(2\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+\beta _{10}q^{3}+(\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
368.2.j.d 368.j 16.e $24$ $2.938$ None \(-4\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
368.2.j.e 368.j 16.e $46$ $2.938$ None \(2\) \(6\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)