Properties

Label 4004.2.m
Level $4004$
Weight $2$
Character orbit 4004.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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4004.2.m.a 4004.m 13.b $2$ $31.972$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
4004.2.m.b 4004.m 13.b $30$ $31.972$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
4004.2.m.c 4004.m 13.b $36$ $31.972$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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