Properties

Label 8028.2.h
Level 8028
Weight 2
Character orbit h
Rep. character \(\chi_{8028}(4013,\cdot)\)
Character field \(\Q\)
Dimension 76
Newforms 1
Sturm bound 2688
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8028.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 669 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2688\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8028, [\chi])\).

Total New Old
Modular forms 1356 76 1280
Cusp forms 1332 76 1256
Eisenstein series 24 0 24

Trace form

\(76q \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(76q \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 100q^{25} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 32q^{37} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 68q^{49} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 8q^{73} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(8028, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8028.2.h.a \(76\) \(64.104\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(8028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(669, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2007, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4014, [\chi])\)\(^{\oplus 2}\)