Properties

Label 4004.2.m
Level 4004
Weight 2
Character orbit m
Rep. character \(\chi_{4004}(2157,\cdot)\)
Character field \(\Q\)
Dimension 68
Newform subspaces 3
Sturm bound 1344
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1344\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4004, [\chi])\).

Total New Old
Modular forms 684 68 616
Cusp forms 660 68 592
Eisenstein series 24 0 24

Trace form

\( 68q + 60q^{9} + O(q^{10}) \) \( 68q + 60q^{9} + 8q^{13} - 4q^{23} - 72q^{25} + 12q^{29} - 4q^{35} - 8q^{39} - 12q^{43} - 68q^{49} + 24q^{51} - 28q^{53} - 16q^{61} - 20q^{65} + 80q^{69} - 40q^{75} + 8q^{77} + 28q^{79} + 68q^{81} + 56q^{87} + 8q^{91} + 44q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4004, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4004.2.m.a \(2\) \(31.972\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+2q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
4004.2.m.b \(30\) \(31.972\) None \(0\) \(0\) \(0\) \(0\)
4004.2.m.c \(36\) \(31.972\) None \(0\) \(-4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(4004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2002, [\chi])\)\(^{\oplus 2}\)