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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1960.2.q.a \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(0\) \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
1960.2.q.b \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1960.2.q.c \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(0\) \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1960.2.q.d \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.e \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.f \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.g \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
1960.2.q.h \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
1960.2.q.i \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
1960.2.q.j \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
1960.2.q.k \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
1960.2.q.l \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
1960.2.q.m \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
1960.2.q.n \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(0\) \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
1960.2.q.o \(2\) \(15.651\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(0\) \(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots\)
1960.2.q.p \(4\) \(15.651\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.q \(4\) \(15.651\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.r \(4\) \(15.651\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1})q^{5}+(-5+\cdots)q^{9}+\cdots\)
1960.2.q.s \(4\) \(15.651\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(-1\) \(-2\) \(0\) \(q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.t \(4\) \(15.651\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(1\) \(2\) \(0\) \(q+\beta _{3}q^{3}+(1-\beta _{1})q^{5}+(-6+5\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.q.u \(4\) \(15.651\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(1\) \(2\) \(0\) \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.2.q.v \(4\) \(15.651\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(2\beta _{1}+2\beta _{3})q^{9}+\cdots\)
1960.2.q.w \(6\) \(15.651\) 6.0.11337408.1 None \(0\) \(0\) \(3\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{3}+\beta _{1}q^{5}+(-3\beta _{1}-\beta _{4}+\cdots)q^{9}+\cdots\)
1960.2.q.x \(8\) \(15.651\) 8.0.\(\cdots\).16 None \(0\) \(-2\) \(-4\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1960.2.q.y \(8\) \(15.651\) 8.0.\(\cdots\).16 None \(0\) \(2\) \(4\) \(0\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)

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

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