Properties

Label 670.2.c
Level $670$
Weight $2$
Character orbit 670.c
Rep. character $\chi_{670}(269,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $2$
Sturm bound $204$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 670 = 2 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 670.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(204\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 106 34 72
Cusp forms 98 34 64
Eisenstein series 8 0 8

Trace form

\( 34 q - 34 q^{4} - 4 q^{5} + 4 q^{6} - 30 q^{9} + O(q^{10}) \) \( 34 q - 34 q^{4} - 4 q^{5} + 4 q^{6} - 30 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{15} + 34 q^{16} + 4 q^{20} + 24 q^{21} - 4 q^{24} + 4 q^{25} - 12 q^{29} + 8 q^{31} + 4 q^{35} + 30 q^{36} - 24 q^{39} - 28 q^{41} + 4 q^{44} + 40 q^{45} + 12 q^{46} - 86 q^{49} + 16 q^{50} - 8 q^{51} - 40 q^{54} + 48 q^{55} + 4 q^{56} - 16 q^{59} + 8 q^{60} + 8 q^{61} - 34 q^{64} + 32 q^{65} - 16 q^{66} + 32 q^{69} + 4 q^{70} + 16 q^{71} + 12 q^{74} + 36 q^{75} - 56 q^{79} - 4 q^{80} + 2 q^{81} - 24 q^{84} - 4 q^{85} + 20 q^{86} - 52 q^{89} - 4 q^{90} + 8 q^{91} + 20 q^{94} + 40 q^{95} + 4 q^{96} - 12 q^{99} + O(q^{100}) \)

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.c.a 670.c 5.b $10$ $5.350$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{8}q^{3}-q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots\)
670.2.c.b 670.c 5.b $24$ $5.350$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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