Properties

Label 4020.2.a
Level 4020
Weight 2
Character orbit a
Rep. character \(\chi_{4020}(1,\cdot)\)
Character field \(\Q\)
Dimension 44
Newform subspaces 9
Sturm bound 1632
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(1632\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4020))\).

Total New Old
Modular forms 828 44 784
Cusp forms 805 44 761
Eisenstein series 23 0 23

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

\(2\)\(3\)\(5\)\(67\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(18\)
Minus space\(-\)\(26\)

Trace form

\( 44q + 44q^{9} + O(q^{10}) \) \( 44q + 44q^{9} - 8q^{11} + 4q^{17} - 4q^{19} - 12q^{23} + 44q^{25} + 4q^{29} - 8q^{31} - 8q^{35} - 12q^{37} - 16q^{41} + 16q^{43} - 4q^{47} + 20q^{49} + 8q^{51} - 8q^{53} - 4q^{59} + 16q^{61} - 8q^{65} - 4q^{67} - 16q^{69} + 8q^{71} + 4q^{73} + 16q^{77} + 24q^{79} + 44q^{81} + 16q^{83} + 8q^{87} - 28q^{89} - 24q^{91} - 8q^{93} - 16q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\) 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 67
4020.2.a.a \(1\) \(32.100\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
4020.2.a.b \(4\) \(32.100\) 4.4.9301.1 None \(0\) \(-4\) \(-4\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4020.2.a.c \(4\) \(32.100\) 4.4.98117.1 None \(0\) \(4\) \(-4\) \(1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
4020.2.a.d \(4\) \(32.100\) \(\Q(\zeta_{15})^+\) None \(0\) \(4\) \(4\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots\)
4020.2.a.e \(5\) \(32.100\) 5.5.1257629.1 None \(0\) \(-5\) \(5\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
4020.2.a.f \(6\) \(32.100\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-6\) \(6\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{5})q^{11}+\cdots\)
4020.2.a.g \(6\) \(32.100\) 6.6.195727752.1 None \(0\) \(6\) \(-6\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(\beta _{1}+\beta _{4})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
4020.2.a.h \(7\) \(32.100\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(-7\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
4020.2.a.i \(7\) \(32.100\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(7\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-\beta _{4}q^{7}+q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(804))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2010))\)\(^{\oplus 2}\)