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Properties

Label 364.2.v
Level $364$
Weight $2$
Character orbit 364.v
Rep. character $\chi_{364}(55,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
Newform subspaces $6$
Sturm bound $112$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 364.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 364 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(112\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\), \(17\)

Dimensions

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

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 48 q^{9} + O(q^{10}) \) \( 104 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 48 q^{9} - 16 q^{14} + 6 q^{16} + 12 q^{18} - 4 q^{21} - 22 q^{22} - 88 q^{25} - 8 q^{28} - 4 q^{29} + 12 q^{30} + 18 q^{32} - 12 q^{36} - 20 q^{37} + 32 q^{42} - 8 q^{44} - 18 q^{49} - 14 q^{50} - 32 q^{53} + 22 q^{56} + 120 q^{57} + 18 q^{58} + 132 q^{60} - 80 q^{64} + 48 q^{65} + 36 q^{70} + 22 q^{72} + 20 q^{74} - 60 q^{77} - 142 q^{78} - 28 q^{81} - 62 q^{84} + 16 q^{85} + 88 q^{86} + 26 q^{88} - 144 q^{92} - 8 q^{93} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.v.a 364.v 364.v $4$ $2.907$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
364.2.v.b 364.v 364.v $4$ $2.907$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
364.2.v.c 364.v 364.v $8$ $2.907$ 8.0.592240896.1 None \(-4\) \(-6\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{3})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\cdots\)
364.2.v.d 364.v 364.v $8$ $2.907$ 8.0.592240896.1 None \(-4\) \(6\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{2}+\beta _{3}+\beta _{7})q^{2}+(1-2\beta _{3}+\cdots)q^{3}+\cdots\)
364.2.v.e 364.v 364.v $8$ $2.907$ 8.0.49787136.1 None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2}-\beta _{4}+\beta _{6})q^{2}+(\beta _{3}-2\beta _{7})q^{3}+\cdots\)
364.2.v.f 364.v 364.v $72$ $2.907$ None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$