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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
360.2.br.a \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-2\) \(-10\) \(q+(-1-\zeta_{12}^{3})q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
360.2.br.b \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(-4\) \(6\) \(-2\) \(8\) \(q+(-1-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2})q^{3}+\cdots\)
360.2.br.c \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(2\) \(8\) \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
360.2.br.d \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(2\) \(-10\) \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
360.2.br.e \(256\) \(2.875\) None \(6\) \(0\) \(0\) \(0\)