Properties

Label 4028.2.a
Level 4028
Weight 2
Character orbit a
Rep. character \(\chi_{4028}(1,\cdot)\)
Character field \(\Q\)
Dimension 78
Newforms 6
Sturm bound 1080
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1080\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4028))\).

Total New Old
Modular forms 546 78 468
Cusp forms 535 78 457
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.

\(2\)\(19\)\(53\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(20\)
\(-\)\(-\)\(-\)\(-\)\(20\)
Plus space\(+\)\(39\)
Minus space\(-\)\(39\)

Trace form

\(78q \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 78q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(78q \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 78q^{9} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 76q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 22q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 10q^{45} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut +\mathstrut 92q^{49} \) \(\mathstrut +\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 50q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 38q^{73} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 70q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 62q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 72q^{91} \) \(\mathstrut -\mathstrut 64q^{93} \) \(\mathstrut -\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4028))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19 53
4028.2.a.a \(1\) \(32.164\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
4028.2.a.b \(1\) \(32.164\) \(\Q\) None \(0\) \(1\) \(2\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots\)
4028.2.a.c \(19\) \(32.164\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(-5\) \(-5\) \(-10\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{10}q^{5}+(-1+\beta _{8})q^{7}+\cdots\)
4028.2.a.d \(19\) \(32.164\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(-4\) \(-2\) \(-11\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(-1+\beta _{11})q^{7}+\cdots\)
4028.2.a.e \(19\) \(32.164\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(3\) \(3\) \(6\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}-\beta _{18}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4028.2.a.f \(19\) \(32.164\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(4\) \(4\) \(13\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(1+\beta _{8})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(212))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2014))\)\(^{\oplus 2}\)