Properties

Label 1470.2.n
Level $1470$
Weight $2$
Character orbit 1470.n
Rep. character $\chi_{1470}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $12$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 12 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 736 80 656
Cusp forms 608 80 528
Eisenstein series 128 0 128

Trace form

\( 80 q + 40 q^{4} + 4 q^{5} - 8 q^{6} + 40 q^{9} + O(q^{10}) \) \( 80 q + 40 q^{4} + 4 q^{5} - 8 q^{6} + 40 q^{9} + 2 q^{10} - 4 q^{11} - 4 q^{15} - 40 q^{16} - 20 q^{19} + 8 q^{20} - 4 q^{24} + 10 q^{25} + 4 q^{26} + 80 q^{29} - 8 q^{30} - 12 q^{31} + 32 q^{34} + 80 q^{36} - 8 q^{39} - 2 q^{40} + 72 q^{41} + 4 q^{44} - 4 q^{45} + 20 q^{46} + 64 q^{50} + 8 q^{51} - 4 q^{54} - 20 q^{55} + 16 q^{59} - 2 q^{60} + 8 q^{61} - 80 q^{64} - 16 q^{65} + 16 q^{66} + 48 q^{69} - 112 q^{71} + 60 q^{74} + 8 q^{75} - 40 q^{76} - 28 q^{79} + 4 q^{80} - 40 q^{81} + 104 q^{85} - 40 q^{86} - 8 q^{89} + 4 q^{90} - 20 q^{94} - 44 q^{95} + 4 q^{96} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1470.2.n.a $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1470.2.n.b $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1470.2.n.c $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1470.2.n.d $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1470.2.n.e $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1470.2.n.f $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1470.2.n.g $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1470.2.n.h $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+(1+\cdots)q^{4}+\cdots\)
1470.2.n.i $4$ $11.738$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+\zeta_{12}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1470.2.n.j $12$ $11.738$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+\beta _{8}q^{4}+\beta _{5}q^{5}+\cdots\)
1470.2.n.k $16$ $11.738$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{2}q^{2}+\beta _{5}q^{3}+(1+\beta _{3})q^{4}-\beta _{7}q^{5}+\cdots\)
1470.2.n.l $16$ $11.738$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{2}q^{2}+\beta _{5}q^{3}+(1+\beta _{3})q^{4}-\beta _{8}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)