Properties

Label 1960.2.q
Level $1960$
Weight $2$
Character orbit 1960.q
Rep. character $\chi_{1960}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $25$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 25 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1960, [\chi])\).

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

Trace form

\( 80 q - 4 q^{3} + 2 q^{5} - 42 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{3} + 2 q^{5} - 42 q^{9} - 2 q^{11} - 16 q^{13} + 4 q^{17} + 2 q^{19} - 40 q^{25} + 32 q^{27} - 4 q^{29} + 16 q^{31} - 4 q^{37} - 32 q^{39} - 8 q^{41} - 64 q^{43} + 12 q^{45} - 12 q^{47} - 8 q^{51} + 4 q^{53} - 8 q^{57} + 4 q^{59} - 2 q^{61} + 6 q^{65} + 20 q^{67} - 4 q^{69} + 64 q^{71} + 12 q^{73} - 4 q^{75} + 12 q^{79} - 16 q^{81} + 88 q^{83} + 44 q^{87} - 14 q^{89} + 60 q^{93} + 8 q^{95} + 16 q^{97} + 92 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1960.2.q.a 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
1960.2.q.b 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1960.2.q.c 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1960.2.q.d 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.e 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.f 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.g 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.h 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
1960.2.q.i 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
1960.2.q.j 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
1960.2.q.k 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
1960.2.q.l 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
1960.2.q.m 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
1960.2.q.n 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
1960.2.q.o 1960.q 7.c $2$ $15.651$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
1960.2.q.p 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.q 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.r 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+(-5+\cdots)q^{9}+\cdots\)
1960.2.q.s 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(-1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.t 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{3}+(1-\beta _{1})q^{5}+(-6+5\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.u 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.2.q.v 1960.q 7.c $4$ $15.651$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(2\beta _{1}+2\beta _{3})q^{9}+\cdots\)
1960.2.q.w 1960.q 7.c $6$ $15.651$ 6.0.11337408.1 None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}-\beta _{5})q^{3}+\beta _{1}q^{5}+(-3\beta _{1}-\beta _{4}+\cdots)q^{9}+\cdots\)
1960.2.q.x 1960.q 7.c $8$ $15.651$ 8.0.\(\cdots\).16 None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.2.q.y 1960.q 7.c $8$ $15.651$ 8.0.\(\cdots\).16 None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)