Properties

Label 364.2.k
Level $364$
Weight $2$
Character orbit 364.k
Rep. character $\chi_{364}(29,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $4$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 364.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(364, [\chi])\).

Total New Old
Modular forms 124 12 112
Cusp forms 100 12 88
Eisenstein series 24 0 24

Trace form

\( 12 q + 4 q^{5} + O(q^{10}) \) \( 12 q + 4 q^{5} - 2 q^{11} + 12 q^{13} + 14 q^{15} - 8 q^{19} - 4 q^{21} - 8 q^{23} + 12 q^{25} - 12 q^{27} + 12 q^{29} - 4 q^{31} - 2 q^{33} + 2 q^{35} - 6 q^{37} + 24 q^{39} - 2 q^{41} + 2 q^{43} + 8 q^{45} - 4 q^{47} - 6 q^{49} - 28 q^{51} - 20 q^{53} - 18 q^{55} + 60 q^{57} + 2 q^{59} - 6 q^{61} - 4 q^{63} - 24 q^{65} - 12 q^{67} + 4 q^{69} - 12 q^{71} + 36 q^{73} - 10 q^{75} - 24 q^{77} - 8 q^{79} + 6 q^{81} - 108 q^{83} + 8 q^{85} - 10 q^{87} - 20 q^{89} - 14 q^{91} - 10 q^{93} - 2 q^{95} + 42 q^{97} + 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(364, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
364.2.k.a 364.k 13.c $2$ $2.907$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
364.2.k.b 364.k 13.c $2$ $2.907$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+3q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
364.2.k.c 364.k 13.c $4$ $2.907$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(-1\) \(6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
364.2.k.d 364.k 13.c $4$ $2.907$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(1\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{3}+(-2+\beta _{2})q^{5}+\beta _{1}q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(364, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(364, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)