Properties

Label 1840.2.m
Level $1840$
Weight $2$
Character orbit 1840.m
Rep. character $\chi_{1840}(1839,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $7$
Sturm bound $576$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 460 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(576\)
Trace bound: \(9\)
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 72 228
Cusp forms 276 72 204
Eisenstein series 24 0 24

Trace form

\( 72q + 72q^{9} + O(q^{10}) \) \( 72q + 72q^{9} + 24q^{29} + 24q^{41} - 96q^{49} + 36q^{69} + 144q^{81} - 72q^{85} + O(q^{100}) \)

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.m.a \(4\) \(14.692\) \(\Q(\sqrt{6}, \sqrt{-14})\) None \(0\) \(-4\) \(0\) \(0\) \(q-q^{3}-\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.b \(4\) \(14.692\) \(\Q(\sqrt{5}, \sqrt{-23})\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots\)
1840.2.m.c \(4\) \(14.692\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+3\beta _{2}q^{7}+\cdots\)
1840.2.m.d \(4\) \(14.692\) \(\Q(\sqrt{6}, \sqrt{-14})\) None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}+\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.e \(8\) \(14.692\) 8.0.\(\cdots\).1 \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots\)
1840.2.m.f \(8\) \(14.692\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{6}q^{5}+2\beta _{5}q^{7}+2q^{9}+\cdots\)
1840.2.m.g \(40\) \(14.692\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)