Properties

Label 8028.2.a
Level 8028
Weight 2
Character orbit a
Rep. character \(\chi_{8028}(1,\cdot)\)
Character field \(\Q\)
Dimension 92
Newforms 16
Sturm bound 2688
Trace bound 7

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Defining parameters

Level: \( N \) = \( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8028.a (trivial)
Character field: \(\Q\)
Newforms: \( 16 \)
Sturm bound: \(2688\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8028))\).

Total New Old
Modular forms 1356 92 1264
Cusp forms 1333 92 1241
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.

\(2\)\(3\)\(223\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(28\)
\(-\)\(-\)\(-\)\(-\)\(28\)
Plus space\(+\)\(46\)
Minus space\(-\)\(46\)

Trace form

\(92q \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(92q \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 90q^{25} \) \(\mathstrut +\mathstrut 4q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 10q^{37} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 102q^{49} \) \(\mathstrut -\mathstrut 10q^{53} \) \(\mathstrut +\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 26q^{71} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8028))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 223
8028.2.a.a \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(q-3q^{5}-2q^{7}-4q^{11}-6q^{17}-8q^{23}+\cdots\)
8028.2.a.b \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{5}-2q^{7}+3q^{11}+6q^{13}+7q^{17}+\cdots\)
8028.2.a.c \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(-\) \(q-q^{5}-2q^{7}-6q^{11}-6q^{13}-4q^{17}+\cdots\)
8028.2.a.d \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q-4q^{7}-3q^{11}-4q^{13}+3q^{17}+2q^{19}+\cdots\)
8028.2.a.e \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+4q^{7}-q^{11}+3q^{17}-6q^{19}+q^{23}+\cdots\)
8028.2.a.f \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(3\) \(-2\) \(-\) \(+\) \(+\) \(q+3q^{5}-2q^{7}+4q^{11}+6q^{17}+8q^{23}+\cdots\)
8028.2.a.g \(2\) \(64.104\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-8\) \(-\) \(+\) \(-\) \(q+\beta q^{5}-4q^{7}-2\beta q^{11}+2q^{13}+2q^{19}+\cdots\)
8028.2.a.h \(2\) \(64.104\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+(1-2\beta )q^{5}+2\beta q^{7}+(4+\beta )q^{11}+\cdots\)
8028.2.a.i \(5\) \(64.104\) 5.5.1710888.1 None \(0\) \(0\) \(6\) \(3\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{4})q^{7}+(3+\cdots)q^{17}+\cdots\)
8028.2.a.j \(7\) \(64.104\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(7\) \(-1\) \(-\) \(-\) \(-\) \(q+(1+\beta _{1}+\beta _{6})q^{5}+(\beta _{3}+\beta _{6})q^{7}+(1+\cdots)q^{11}+\cdots\)
8028.2.a.k \(8\) \(64.104\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-5\) \(5\) \(-\) \(-\) \(+\) \(q+(-\beta _{2}+\beta _{3}+\beta _{6}+\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
8028.2.a.l \(8\) \(64.104\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(5\) \(-13\) \(-\) \(-\) \(+\) \(q+(\beta _{4}-\beta _{5})q^{5}+(-2+\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
8028.2.a.m \(11\) \(64.104\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(-5\) \(-5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{5}-\beta _{10}q^{7}+\beta _{7}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8028.2.a.n \(11\) \(64.104\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(-5\) \(11\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{5}+(1+\beta _{9})q^{7}-\beta _{5}q^{11}+(1+\cdots)q^{13}+\cdots\)
8028.2.a.o \(16\) \(64.104\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{15}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8028.2.a.p \(16\) \(64.104\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(22\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{5}+(1-\beta _{7})q^{7}+\beta _{9}q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(892))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\)\(^{\oplus 2}\)