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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1840.2.e.a \(2\) \(14.692\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{3}+(2+i)q^{5}-3iq^{7}-q^{9}+\cdots\)
1840.2.e.b \(2\) \(14.692\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{3}+(2+i)q^{5}-iq^{7}-q^{9}-2iq^{13}+\cdots\)
1840.2.e.c \(4\) \(14.692\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(1+2\beta _{2})q^{5}+(3\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1840.2.e.d \(8\) \(14.692\) 8.0.527896576.2 None \(0\) \(0\) \(-6\) \(0\) \(q+(-\beta _{1}+\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
1840.2.e.e \(8\) \(14.692\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1840.2.e.f \(12\) \(14.692\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{6})q^{3}-\beta _{8}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
1840.2.e.g \(14\) \(14.692\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{8}q^{3}-\beta _{5}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
1840.2.e.h \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{5}q^{3}-\beta _{10}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots\)

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

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