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Properties

Label 210.2.u
Level $210$
Weight $2$
Character orbit 210.u
Rep. character $\chi_{210}(73,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $32$
Newform subspaces $2$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.u (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).

Total New Old
Modular forms 224 32 192
Cusp forms 160 32 128
Eisenstein series 64 0 64

Trace form

\( 32 q + 24 q^{5} - 12 q^{7} + O(q^{10}) \) \( 32 q + 24 q^{5} - 12 q^{7} + 12 q^{10} + 8 q^{11} + 8 q^{15} + 16 q^{16} + 16 q^{21} + 8 q^{22} - 8 q^{23} - 16 q^{25} - 24 q^{26} - 12 q^{28} - 8 q^{30} - 48 q^{31} + 12 q^{33} - 40 q^{35} - 32 q^{36} - 16 q^{37} - 48 q^{38} + 4 q^{42} - 48 q^{43} - 8 q^{46} - 24 q^{47} + 16 q^{51} + 16 q^{53} + 16 q^{56} - 16 q^{57} + 36 q^{58} + 48 q^{61} + 32 q^{65} - 48 q^{67} + 36 q^{70} - 64 q^{71} - 24 q^{73} - 48 q^{75} - 32 q^{78} + 24 q^{80} + 16 q^{81} + 48 q^{82} + 16 q^{85} - 16 q^{86} + 60 q^{87} + 4 q^{88} + 16 q^{91} + 16 q^{92} + 8 q^{93} + 24 q^{95} + 16 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
210.2.u.a 210.u 35.k $16$ $1.677$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{12}q^{2}-\beta _{6}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
210.2.u.b 210.u 35.k $16$ $1.677$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{2}q^{2}-\beta _{15}q^{3}-\beta _{5}q^{4}+(1+2\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

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