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Properties

Label 360.2.br
Level $360$
Weight $2$
Character orbit 360.br
Rep. character $\chi_{360}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $272$
Newform subspaces $5$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 360 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(360, [\chi])\).

Total New Old
Modular forms 304 304 0
Cusp forms 272 272 0
Eisenstein series 32 32 0

Trace form

\( 272 q - 6 q^{2} - 8 q^{6} - 4 q^{7} + O(q^{10}) \) \( 272 q - 6 q^{2} - 8 q^{6} - 4 q^{7} - 8 q^{10} + 2 q^{12} - 8 q^{15} - 4 q^{16} - 28 q^{18} - 6 q^{20} + 6 q^{22} - 12 q^{23} - 4 q^{25} - 24 q^{28} + 26 q^{30} - 8 q^{31} - 66 q^{32} + 4 q^{33} - 40 q^{36} - 18 q^{38} - 2 q^{40} - 24 q^{41} - 34 q^{42} + 8 q^{46} - 12 q^{47} - 50 q^{48} - 6 q^{50} + 14 q^{52} + 24 q^{55} - 96 q^{56} - 32 q^{57} - 10 q^{58} - 2 q^{60} - 36 q^{63} - 12 q^{65} + 20 q^{66} - 30 q^{68} - 22 q^{70} - 86 q^{72} - 16 q^{73} - 8 q^{76} - 10 q^{78} - 16 q^{82} + 96 q^{86} - 76 q^{87} + 6 q^{88} + 78 q^{90} - 120 q^{92} - 72 q^{95} - 68 q^{96} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.2.br.a 360.br 360.ar $4$ $2.875$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
360.2.br.b 360.br 360.ar $4$ $2.875$ \(\Q(\zeta_{12})\) None \(-4\) \(6\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2})q^{3}+\cdots\)
360.2.br.c 360.br 360.ar $4$ $2.875$ \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(2\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
360.2.br.d 360.br 360.ar $4$ $2.875$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(2\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
360.2.br.e 360.br 360.ar $256$ $2.875$ None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$