Properties

Label 4016.2.a
Level 4016
Weight 2
Character orbit a
Rep. character \(\chi_{4016}(1,\cdot)\)
Character field \(\Q\)
Dimension 125
Newform subspaces 13
Sturm bound 1008
Trace bound 3

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Defining parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1008\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4016))\).

Total New Old
Modular forms 510 125 385
Cusp forms 499 125 374
Eisenstein series 11 0 11

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

\(2\)\(251\)FrickeDim.
\(+\)\(+\)\(+\)\(21\)
\(+\)\(-\)\(-\)\(42\)
\(-\)\(+\)\(-\)\(31\)
\(-\)\(-\)\(+\)\(31\)
Plus space\(+\)\(52\)
Minus space\(-\)\(73\)

Trace form

\( 125q + 2q^{3} - 2q^{5} + 2q^{7} + 125q^{9} + O(q^{10}) \) \( 125q + 2q^{3} - 2q^{5} + 2q^{7} + 125q^{9} - 4q^{11} - 2q^{13} - 4q^{15} + 2q^{17} - 4q^{19} - 8q^{21} - 10q^{23} + 127q^{25} - 4q^{27} - 2q^{29} + 2q^{31} - 2q^{37} + 8q^{39} + 2q^{41} - 4q^{43} - 18q^{45} - 12q^{47} + 133q^{49} + 28q^{51} - 2q^{53} + 8q^{55} + 8q^{57} - 12q^{59} - 2q^{61} + 6q^{63} + 12q^{65} + 2q^{67} - 8q^{69} + 32q^{71} + 18q^{73} - 2q^{75} - 16q^{77} - 10q^{79} + 133q^{81} + 10q^{83} - 12q^{85} + 48q^{87} + 10q^{89} + 56q^{91} - 8q^{93} - 8q^{95} + 2q^{97} + 40q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4016))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 251
4016.2.a.a \(2\) \(32.068\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(5\) \(2\) \(-\) \(-\) \(q-q^{3}+(2+\beta )q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
4016.2.a.b \(2\) \(32.068\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-3\) \(4\) \(-\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}+(1+2\beta )q^{7}-2q^{9}+\cdots\)
4016.2.a.c \(4\) \(32.068\) 4.4.725.1 None \(0\) \(2\) \(-3\) \(3\) \(-\) \(-\) \(q+\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
4016.2.a.d \(5\) \(32.068\) 5.5.138917.1 None \(0\) \(-2\) \(7\) \(-1\) \(-\) \(+\) \(q+\beta _{4}q^{3}+(2+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
4016.2.a.e \(5\) \(32.068\) 5.5.242773.1 None \(0\) \(1\) \(-6\) \(1\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
4016.2.a.f \(6\) \(32.068\) 6.6.60853001.1 None \(0\) \(-1\) \(-1\) \(-6\) \(-\) \(-\) \(q+\beta _{4}q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4016.2.a.g \(7\) \(32.068\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(-2\) \(6\) \(-\) \(+\) \(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4016.2.a.h \(9\) \(32.068\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(1\) \(-5\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+(-\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots\)
4016.2.a.i \(12\) \(32.068\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(5\) \(-5\) \(+\) \(+\) \(q-\beta _{1}q^{3}+\beta _{8}q^{5}-\beta _{5}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4016.2.a.j \(14\) \(32.068\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-3\) \(-2\) \(-8\) \(-\) \(-\) \(q-\beta _{1}q^{3}+\beta _{4}q^{5}+(-1+\beta _{9})q^{7}+(1+\cdots)q^{9}+\cdots\)
4016.2.a.k \(17\) \(32.068\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(0\) \(0\) \(3\) \(-3\) \(-\) \(+\) \(q+\beta _{4}q^{3}+\beta _{6}q^{5}+\beta _{13}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
4016.2.a.l \(19\) \(32.068\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(6\) \(-8\) \(11\) \(+\) \(-\) \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(1+\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
4016.2.a.m \(23\) \(32.068\) None \(0\) \(-2\) \(8\) \(-2\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2008))\)\(^{\oplus 2}\)