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Properties

Label 210.3.p
Level $210$
Weight $3$
Character orbit 210.p
Rep. character $\chi_{210}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 32 176
Cusp forms 176 32 144
Eisenstein series 32 0 32

Trace form

\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} + O(q^{10}) \) \( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.p.a 210.p 35.i $32$ $5.722$ None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)