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Properties

Label 828.2.m
Level $828$
Weight $2$
Character orbit 828.m
Rep. character $\chi_{828}(367,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Newform subspaces $4$
Sturm bound $288$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 828.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 828 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

Trace form

\( 280 q - 2 q^{2} - 2 q^{4} - 11 q^{6} - 14 q^{8} - 8 q^{9} + O(q^{10}) \) \( 280 q - 2 q^{2} - 2 q^{4} - 11 q^{6} - 14 q^{8} - 8 q^{9} - 4 q^{12} - 4 q^{13} - 2 q^{16} - 3 q^{18} + 8 q^{24} + 120 q^{25} + 12 q^{26} + 4 q^{29} - 2 q^{32} - 33 q^{36} - 4 q^{41} + 4 q^{46} - 22 q^{48} - 120 q^{49} + 42 q^{50} + 5 q^{52} - 34 q^{54} - 3 q^{58} - 22 q^{62} + 34 q^{64} + 14 q^{69} - 32 q^{70} - 6 q^{72} - 16 q^{73} + 36 q^{77} + 67 q^{78} - 16 q^{81} - 18 q^{82} + 16 q^{85} + 28 q^{92} - 108 q^{93} - q^{94} - 55 q^{96} + 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
828.2.m.a 828.m 828.m $8$ $6.612$ 8.0.303595776.1 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3}+\beta _{4})q^{2}+(\beta _{3}-\beta _{5})q^{3}+2\beta _{5}q^{4}+\cdots\)
828.2.m.b 828.m 828.m $12$ $6.612$ 12.0.\(\cdots\).2 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\beta _{11}q^{2}+(\beta _{3}-\beta _{10})q^{3}+(-\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
828.2.m.c 828.m 828.m $12$ $6.612$ 12.0.\(\cdots\).2 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{2}q^{2}-\beta _{5}q^{3}+(\beta _{8}-\beta _{9})q^{4}+\beta _{7}q^{6}+\cdots\)
828.2.m.d 828.m 828.m $248$ $6.612$ None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$