Properties

Label 210.3.q
Level $210$
Weight $3$
Character orbit 210.q
Rep. character $\chi_{210}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(210, [\chi])\).

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64 q - 64 q^{4} + 8 q^{6} - 4 q^{9} + O(q^{10}) \) \( 64 q - 64 q^{4} + 8 q^{6} - 4 q^{9} - 8 q^{10} + 4 q^{15} - 128 q^{16} + 8 q^{19} - 88 q^{21} - 8 q^{24} + 12 q^{25} - 8 q^{30} + 152 q^{31} + 16 q^{36} - 208 q^{39} - 16 q^{40} + 106 q^{45} - 56 q^{46} - 64 q^{49} - 140 q^{51} - 56 q^{54} + 616 q^{55} - 4 q^{60} + 104 q^{61} + 512 q^{64} - 160 q^{66} + 456 q^{69} - 144 q^{70} + 298 q^{75} - 32 q^{76} - 360 q^{79} + 304 q^{81} - 80 q^{84} - 408 q^{85} - 688 q^{90} - 288 q^{91} + 240 q^{94} - 16 q^{96} - 568 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
210.3.q.a 210.q 105.o $64$ $5.722$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)