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Properties

Label 316.2.m
Level $316$
Weight $2$
Character orbit 316.m
Rep. character $\chi_{316}(5,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $168$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 316 = 2^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 316.m (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 79 \)
Character field: \(\Q(\zeta_{39})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(316, [\chi])\).

Total New Old
Modular forms 1032 168 864
Cusp forms 888 168 720
Eisenstein series 144 0 144

Trace form

\( 168 q + q^{3} + q^{7} + 10 q^{9} + O(q^{10}) \) \( 168 q + q^{3} + q^{7} + 10 q^{9} - 6 q^{11} - 2 q^{13} + 28 q^{15} + 2 q^{17} + 5 q^{19} + 34 q^{21} - q^{23} - 23 q^{25} + 37 q^{27} + 4 q^{29} - 38 q^{31} + 28 q^{33} + 32 q^{35} - 43 q^{37} - 50 q^{39} - 20 q^{41} - 7 q^{43} - 11 q^{45} + 23 q^{47} + 28 q^{49} - 10 q^{51} - 7 q^{53} + 24 q^{55} - 86 q^{57} - 48 q^{59} - 40 q^{61} - 11 q^{63} - 52 q^{65} + 27 q^{67} - 176 q^{69} - 16 q^{71} - 88 q^{73} - 85 q^{75} - 70 q^{77} - 170 q^{79} - 113 q^{81} - 186 q^{83} - 118 q^{85} - 77 q^{87} - 6 q^{89} - 39 q^{91} - 29 q^{93} - 58 q^{95} - 51 q^{97} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(316, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
316.2.m.a 316.m 79.g $168$ $2.523$ None \(0\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{39}]$

Decomposition of \(S_{2}^{\mathrm{old}}(316, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(316, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(158, [\chi])\)\(^{\oplus 2}\)