Properties

Label 4028.2.c
Level 4028
Weight 2
Character orbit c
Rep. character \(\chi_{4028}(3497,\cdot)\)
Character field \(\Q\)
Dimension 82
Newform subspaces 1
Sturm bound 1080
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 53 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(1080\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4028, [\chi])\).

Total New Old
Modular forms 546 82 464
Cusp forms 534 82 452
Eisenstein series 12 0 12

Trace form

\( 82q - 8q^{7} - 82q^{9} + O(q^{10}) \) \( 82q - 8q^{7} - 82q^{9} + 4q^{13} + 4q^{15} - 4q^{17} - 58q^{25} - 16q^{29} - 12q^{37} - 32q^{43} + 8q^{47} + 98q^{49} + 6q^{53} - 4q^{57} + 4q^{59} + 8q^{63} + 28q^{69} - 8q^{77} + 154q^{81} - 20q^{89} + 48q^{91} - 56q^{93} - 44q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4028, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4028.2.c.a \(82\) \(32.164\) None \(0\) \(0\) \(0\) \(-8\)

Decomposition of \(S_{2}^{\mathrm{old}}(4028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(212, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1007, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2014, [\chi])\)\(^{\oplus 2}\)