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Properties

Label 210.3.v
Level $210$
Weight $3$
Character orbit 210.v
Rep. character $\chi_{210}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $64$
Newform subspaces $2$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 416 64 352
Cusp forms 352 64 288
Eisenstein series 64 0 64

Trace form

\( 64 q - 8 q^{5} + 16 q^{7} + O(q^{10}) \) \( 64 q - 8 q^{5} + 16 q^{7} + 16 q^{10} - 16 q^{11} + 48 q^{15} + 128 q^{16} - 112 q^{17} - 48 q^{21} + 96 q^{22} - 48 q^{23} + 40 q^{25} + 64 q^{26} + 112 q^{28} + 48 q^{30} + 272 q^{31} + 24 q^{33} + 40 q^{35} + 384 q^{36} - 8 q^{37} - 64 q^{38} - 416 q^{41} - 48 q^{42} - 496 q^{43} - 96 q^{46} - 440 q^{47} + 48 q^{51} - 48 q^{53} - 208 q^{55} + 128 q^{56} + 192 q^{57} - 208 q^{58} + 432 q^{61} - 96 q^{62} + 120 q^{63} - 136 q^{65} + 128 q^{67} + 224 q^{68} - 288 q^{70} - 480 q^{71} + 136 q^{73} - 96 q^{75} + 256 q^{76} - 1160 q^{77} - 192 q^{78} + 32 q^{80} + 288 q^{81} - 128 q^{82} - 1152 q^{83} + 464 q^{85} - 128 q^{86} - 144 q^{87} + 96 q^{88} + 720 q^{91} + 192 q^{92} - 48 q^{93} + 440 q^{95} + 80 q^{97} - 128 q^{98} + O(q^{100}) \)

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.v.a 210.v 35.l $32$ $5.722$ None \(-16\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
210.3.v.b 210.v 35.l $32$ $5.722$ None \(16\) \(0\) \(-8\) \(24\) $\mathrm{SU}(2)[C_{12}]$

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

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