Properties

Label 3240.2.a
Level $3240$
Weight $2$
Character orbit 3240.a
Rep. character $\chi_{3240}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $22$
Sturm bound $1296$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1296\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3240))\).

Total New Old
Modular forms 696 48 648
Cusp forms 601 48 553
Eisenstein series 95 0 95

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.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(20\)
Minus space\(-\)\(28\)

Trace form

\( 48q + O(q^{10}) \) \( 48q - 12q^{19} + 48q^{25} + 24q^{31} + 12q^{43} + 36q^{49} - 12q^{61} - 12q^{67} + 36q^{73} + 48q^{91} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3240))\) 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
3240.2.a.a \(1\) \(25.872\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{5}-2q^{7}+3q^{11}-2q^{17}+q^{19}+\cdots\)
3240.2.a.b \(1\) \(25.872\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{5}-5q^{11}+3q^{17}+5q^{19}+6q^{23}+\cdots\)
3240.2.a.c \(1\) \(25.872\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{5}+q^{11}-7q^{19}+6q^{23}+q^{25}+\cdots\)
3240.2.a.d \(1\) \(25.872\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{5}-2q^{7}-3q^{11}+2q^{17}+q^{19}+\cdots\)
3240.2.a.e \(1\) \(25.872\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(q+q^{5}-q^{11}-7q^{19}-6q^{23}+q^{25}+\cdots\)
3240.2.a.f \(1\) \(25.872\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{5}+5q^{11}-3q^{17}+5q^{19}-6q^{23}+\cdots\)
3240.2.a.g \(2\) \(25.872\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(q-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
3240.2.a.h \(2\) \(25.872\) \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(+\) \(q-q^{5}+\beta q^{7}+(-3+\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
3240.2.a.i \(2\) \(25.872\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(+\) \(+\) \(q-q^{5}+\beta q^{7}+(1-\beta )q^{11}-\beta q^{13}+\cdots\)
3240.2.a.j \(2\) \(25.872\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(+\) \(q-q^{5}+(1+\beta )q^{7}-2q^{17}+(-2-2\beta )q^{19}+\cdots\)
3240.2.a.k \(2\) \(25.872\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(4\) \(-\) \(+\) \(+\) \(q-q^{5}+(2+\beta )q^{7}+(2+2\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
3240.2.a.l \(2\) \(25.872\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{5}+(-1+\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
3240.2.a.m \(2\) \(25.872\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(1\) \(+\) \(+\) \(-\) \(q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}-\beta q^{13}+\cdots\)
3240.2.a.n \(2\) \(25.872\) \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(2\) \(1\) \(+\) \(+\) \(-\) \(q+q^{5}+\beta q^{7}+(3-\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
3240.2.a.o \(2\) \(25.872\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{5}+(1+\beta )q^{7}+2q^{17}+(-2-2\beta )q^{19}+\cdots\)
3240.2.a.p \(2\) \(25.872\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(4\) \(+\) \(-\) \(-\) \(q+q^{5}+(2+\beta )q^{7}+(-2-2\beta )q^{11}+\cdots\)
3240.2.a.q \(3\) \(25.872\) 3.3.564.1 None \(0\) \(0\) \(-3\) \(-5\) \(+\) \(-\) \(+\) \(q-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
3240.2.a.r \(3\) \(25.872\) 3.3.564.1 None \(0\) \(0\) \(3\) \(-5\) \(-\) \(+\) \(-\) \(q+q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
3240.2.a.s \(4\) \(25.872\) 4.4.29268.1 None \(0\) \(0\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{5}-\beta _{2}q^{7}+(\beta _{2}+\beta _{3})q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)
3240.2.a.t \(4\) \(25.872\) 4.4.62352.1 None \(0\) \(0\) \(-4\) \(2\) \(+\) \(-\) \(+\) \(q-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-2+\beta _{1}-\beta _{3})q^{11}+\cdots\)
3240.2.a.u \(4\) \(25.872\) 4.4.29268.1 None \(0\) \(0\) \(4\) \(-1\) \(+\) \(+\) \(-\) \(q+q^{5}-\beta _{2}q^{7}+(-\beta _{2}-\beta _{3})q^{11}+(1+\cdots)q^{13}+\cdots\)
3240.2.a.v \(4\) \(25.872\) 4.4.62352.1 None \(0\) \(0\) \(4\) \(2\) \(-\) \(-\) \(-\) \(q+q^{5}+(\beta _{1}-\beta _{2})q^{7}+(2-\beta _{1}+\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(810))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1620))\)\(^{\oplus 2}\)