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Properties

Label 670.2.m
Level $670$
Weight $2$
Character orbit 670.m
Rep. character $\chi_{670}(97,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $136$
Newform subspaces $1$
Sturm bound $204$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 670.m (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 335 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(204\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(670, [\chi])\).

Total New Old
Modular forms 424 136 288
Cusp forms 392 136 256
Eisenstein series 32 0 32

Trace form

\( 136 q + 4 q^{6} + O(q^{10}) \) \( 136 q + 4 q^{6} - 8 q^{15} + 68 q^{16} - 12 q^{20} - 20 q^{21} - 8 q^{23} + 24 q^{25} - 12 q^{35} - 64 q^{36} - 24 q^{37} + 24 q^{38} - 12 q^{41} - 12 q^{46} - 24 q^{47} + 72 q^{50} - 48 q^{51} + 24 q^{55} - 4 q^{56} - 36 q^{57} - 12 q^{60} + 24 q^{61} + 32 q^{62} - 68 q^{67} - 88 q^{71} + 16 q^{73} + 32 q^{76} + 28 q^{77} + 60 q^{78} + 56 q^{81} - 48 q^{82} + 16 q^{83} + 96 q^{85} - 4 q^{86} - 96 q^{87} + 32 q^{90} + 128 q^{91} - 16 q^{92} - 36 q^{93} - 60 q^{95} - 4 q^{96} - 120 q^{97} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(670, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
670.2.m.a 670.m 335.m $136$ $5.350$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(670, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(670, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)