Properties

Label 1960.2.g
Level $1960$
Weight $2$
Character orbit 1960.g
Rep. character $\chi_{1960}(1569,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $7$
Sturm bound $672$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(672\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(19\)

Dimensions

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

Total New Old
Modular forms 368 62 306
Cusp forms 304 62 242
Eisenstein series 64 0 64

Trace form

\( 62q - 2q^{5} - 66q^{9} + O(q^{10}) \) \( 62q - 2q^{5} - 66q^{9} - 4q^{11} + 4q^{15} - 8q^{19} + 14q^{25} + 8q^{29} - 8q^{31} + 24q^{39} - 20q^{41} + 18q^{45} - 48q^{51} + 8q^{55} - 20q^{61} + 16q^{65} + 32q^{69} + 48q^{75} + 40q^{79} + 86q^{81} + 16q^{85} + 36q^{89} - 20q^{95} + 12q^{99} + O(q^{100}) \)

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.g.a \(2\) \(15.651\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}+2q^{9}-q^{11}+\cdots\)
1960.2.g.b \(2\) \(15.651\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
1960.2.g.c \(6\) \(15.651\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1960.2.g.d \(8\) \(15.651\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
1960.2.g.e \(12\) \(15.651\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
1960.2.g.f \(12\) \(15.651\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
1960.2.g.g \(20\) \(15.651\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{17}q^{3}-\beta _{16}q^{5}+(-1+\beta _{1})q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)