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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1840.2.m.a 1840.m 460.g $4$ $14.692$ \(\Q(\sqrt{6}, \sqrt{-14})\) None 1840.2.m.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.b 1840.m 460.g $4$ $14.692$ \(\Q(\sqrt{5}, \sqrt{-23})\) \(\Q(\sqrt{-115}) \) 1840.2.m.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots\)
1840.2.m.c 1840.m 460.g $4$ $14.692$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) 1840.2.m.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+3\beta _{2}q^{7}+\cdots\)
1840.2.m.d 1840.m 460.g $4$ $14.692$ \(\Q(\sqrt{6}, \sqrt{-14})\) None 1840.2.m.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.e 1840.m 460.g $8$ $14.692$ 8.0.\(\cdots\).1 \(\Q(\sqrt{-115}) \) 1840.2.m.e \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots\)
1840.2.m.f 1840.m 460.g $8$ $14.692$ 8.0.40960000.1 None 1840.2.m.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{6}q^{5}+2\beta _{5}q^{7}+2q^{9}+\cdots\)
1840.2.m.g 1840.m 460.g $40$ $14.692$ None 1840.2.m.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)