Properties

Label 1620.2.a
Level $1620$
Weight $2$
Character orbit 1620.a
Rep. character $\chi_{1620}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $10$
Sturm bound $648$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(648\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1620))\).

Total New Old
Modular forms 360 16 344
Cusp forms 289 16 273
Eisenstein series 71 0 71

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

\(2\)\(3\)\(5\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(6\)
Minus space\(-\)\(10\)

Trace form

\( 16q - 4q^{7} + O(q^{10}) \) \( 16q - 4q^{7} - 4q^{13} + 8q^{19} + 16q^{25} + 8q^{31} - 4q^{37} + 20q^{43} + 24q^{49} + 32q^{61} + 32q^{67} + 32q^{73} - 16q^{79} - 12q^{85} - 8q^{91} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1620))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
1620.2.a.a \(1\) \(12.936\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{5}-4q^{7}-3q^{11}-4q^{13}+5q^{19}+\cdots\)
1620.2.a.b \(1\) \(12.936\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{5}-q^{7}-4q^{13}+6q^{17}+2q^{19}+\cdots\)
1620.2.a.c \(1\) \(12.936\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q-q^{5}+2q^{7}+3q^{11}-4q^{13}+6q^{17}+\cdots\)
1620.2.a.d \(1\) \(12.936\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{5}-4q^{7}+3q^{11}-4q^{13}+5q^{19}+\cdots\)
1620.2.a.e \(1\) \(12.936\) \(\Q\) None \(0\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{5}-q^{7}-4q^{13}-6q^{17}+2q^{19}+\cdots\)
1620.2.a.f \(1\) \(12.936\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(+\) \(-\) \(q+q^{5}+2q^{7}-3q^{11}-4q^{13}-6q^{17}+\cdots\)
1620.2.a.g \(2\) \(12.936\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(q-q^{5}+(-1+\beta )q^{7}-\beta q^{11}+(2-2\beta )q^{13}+\cdots\)
1620.2.a.h \(2\) \(12.936\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{5}+(-1+\beta )q^{7}+\beta q^{11}+(2-2\beta )q^{13}+\cdots\)
1620.2.a.i \(3\) \(12.936\) 3.3.564.1 None \(0\) \(0\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(q-q^{5}+(1-\beta _{1})q^{7}-\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots\)
1620.2.a.j \(3\) \(12.936\) 3.3.564.1 None \(0\) \(0\) \(3\) \(3\) \(-\) \(-\) \(-\) \(q+q^{5}+(1-\beta _{1})q^{7}+\beta _{2}q^{11}+(2+\beta _{2})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1620))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1620)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(810))\)\(^{\oplus 2}\)