Properties

Label 1840.2.e
Level $1840$
Weight $2$
Character orbit 1840.e
Rep. character $\chi_{1840}(369,\cdot)$
Character field $\Q$
Dimension $66$
Newform subspaces $8$
Sturm bound $576$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(576\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

Total New Old
Modular forms 300 66 234
Cusp forms 276 66 210
Eisenstein series 24 0 24

Trace form

\( 66 q + 2 q^{5} - 66 q^{9} + O(q^{10}) \) \( 66 q + 2 q^{5} - 66 q^{9} + 10 q^{25} - 4 q^{29} + 12 q^{31} - 12 q^{35} - 40 q^{39} - 4 q^{41} - 10 q^{45} - 82 q^{49} + 24 q^{51} + 16 q^{55} + 52 q^{59} + 20 q^{61} - 8 q^{65} + 36 q^{71} - 48 q^{75} - 48 q^{79} + 66 q^{81} - 8 q^{85} + 20 q^{89} + 32 q^{91} - 48 q^{95} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1840.2.e.a 1840.e 5.b $2$ $14.692$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+(2+i)q^{5}-3iq^{7}-q^{9}+\cdots\)
1840.2.e.b 1840.e 5.b $2$ $14.692$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+(2+i)q^{5}-iq^{7}-q^{9}-2iq^{13}+\cdots\)
1840.2.e.c 1840.e 5.b $4$ $14.692$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(1+2\beta _{2})q^{5}+(3\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1840.2.e.d 1840.e 5.b $8$ $14.692$ 8.0.527896576.2 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
1840.2.e.e 1840.e 5.b $8$ $14.692$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1840.2.e.f 1840.e 5.b $12$ $14.692$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{5}+\beta _{6})q^{3}-\beta _{8}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
1840.2.e.g 1840.e 5.b $14$ $14.692$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{3}-\beta _{5}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
1840.2.e.h 1840.e 5.b $16$ $14.692$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}-\beta _{10}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)