Properties

Label 1470.2.i
Level $1470$
Weight $2$
Character orbit 1470.i
Rep. character $\chi_{1470}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $24$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 24 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(31\)

Dimensions

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

Total New Old
Modular forms 736 56 680
Cusp forms 608 56 552
Eisenstein series 128 0 128

Trace form

\( 56 q - 28 q^{4} - 28 q^{9} + O(q^{10}) \) \( 56 q - 28 q^{4} - 28 q^{9} + 4 q^{10} - 4 q^{11} - 16 q^{13} - 28 q^{16} - 8 q^{17} - 4 q^{19} + 16 q^{22} - 28 q^{25} - 4 q^{26} + 32 q^{29} - 8 q^{31} + 8 q^{33} + 16 q^{34} + 56 q^{36} - 48 q^{37} - 8 q^{38} - 40 q^{39} + 4 q^{40} - 24 q^{41} + 48 q^{43} - 4 q^{44} + 12 q^{46} - 16 q^{47} + 8 q^{51} + 8 q^{52} - 24 q^{53} + 16 q^{55} + 80 q^{57} + 8 q^{58} + 32 q^{59} + 8 q^{61} - 32 q^{62} + 56 q^{64} - 4 q^{65} - 40 q^{67} - 8 q^{68} + 32 q^{69} + 32 q^{71} - 8 q^{73} - 4 q^{74} + 8 q^{76} - 32 q^{78} - 56 q^{79} - 28 q^{81} + 16 q^{82} - 16 q^{83} + 16 q^{85} - 8 q^{88} + 8 q^{89} - 8 q^{90} - 56 q^{93} - 12 q^{94} + 64 q^{97} + 8 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1470.2.i.a 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.b 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.c 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.d 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.e 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.f 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.g 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.h 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.i 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.j 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.k 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.l 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.m 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.n 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.o 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.p 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.q 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.r 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.s 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.t 1470.i 7.c $2$ $11.738$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1470.2.i.u 1470.i 7.c $4$ $11.738$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
1470.2.i.v 1470.i 7.c $4$ $11.738$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
1470.2.i.w 1470.i 7.c $4$ $11.738$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
1470.2.i.x 1470.i 7.c $4$ $11.738$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)