Properties

Label 1960.2.a
Level $1960$
Weight $2$
Character orbit 1960.a
Rep. character $\chi_{1960}(1,\cdot)$
Character field $\Q$
Dimension $41$
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.a (trivial)
Character field: \(\Q\)
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 \(M_{2}(\Gamma_0(1960))\).

Total New Old
Modular forms 368 41 327
Cusp forms 305 41 264
Eisenstein series 63 0 63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(18\)
Minus space\(-\)\(23\)

Trace form

\( 41q + 4q^{3} - q^{5} + 33q^{9} + O(q^{10}) \) \( 41q + 4q^{3} - q^{5} + 33q^{9} + 2q^{13} - 14q^{17} + 8q^{19} + 4q^{23} + 41q^{25} + 16q^{27} + 2q^{29} + 24q^{31} - 24q^{33} - 2q^{37} + 8q^{39} + 2q^{41} + 8q^{43} + 3q^{45} - 20q^{47} + 8q^{51} + 14q^{53} + 4q^{55} + 8q^{57} - 8q^{59} + 18q^{61} + 10q^{65} + 40q^{69} - 16q^{71} - 6q^{73} + 4q^{75} + q^{81} + 4q^{83} + 2q^{85} + 16q^{87} + 2q^{89} + 24q^{93} - 4q^{95} - 30q^{97} + 112q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
1960.2.a.a \(1\) \(15.651\) \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q-2q^{3}-q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
1960.2.a.b \(1\) \(15.651\) \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1960.2.a.c \(1\) \(15.651\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{9}-2q^{11}+4q^{13}+\cdots\)
1960.2.a.d \(1\) \(15.651\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{9}-5q^{11}-7q^{13}+\cdots\)
1960.2.a.e \(1\) \(15.651\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots\)
1960.2.a.f \(1\) \(15.651\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
1960.2.a.g \(1\) \(15.651\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
1960.2.a.h \(1\) \(15.651\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{9}-5q^{11}+7q^{13}+\cdots\)
1960.2.a.i \(1\) \(15.651\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots\)
1960.2.a.j \(1\) \(15.651\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots\)
1960.2.a.k \(1\) \(15.651\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots\)
1960.2.a.l \(1\) \(15.651\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{5}-2q^{9}-2q^{11}-4q^{13}+\cdots\)
1960.2.a.m \(1\) \(15.651\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+\cdots\)
1960.2.a.n \(1\) \(15.651\) \(\Q\) None \(0\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1960.2.a.o \(1\) \(15.651\) \(\Q\) None \(0\) \(3\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q+3q^{3}-q^{5}+6q^{9}-5q^{11}+5q^{13}+\cdots\)
1960.2.a.p \(2\) \(15.651\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
1960.2.a.q \(2\) \(15.651\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}-q^{11}+\cdots\)
1960.2.a.r \(2\) \(15.651\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
1960.2.a.s \(2\) \(15.651\) \(\Q(\sqrt{33}) \) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+q^{5}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
1960.2.a.t \(2\) \(15.651\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
1960.2.a.u \(2\) \(15.651\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
1960.2.a.v \(3\) \(15.651\) 3.3.1944.1 None \(0\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
1960.2.a.w \(3\) \(15.651\) 3.3.1944.1 None \(0\) \(0\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
1960.2.a.x \(4\) \(15.651\) 4.4.16448.2 None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1960.2.a.y \(4\) \(15.651\) 4.4.16448.2 None \(0\) \(2\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 2}\)