Properties

Label 1840.2.i
Level $1840$
Weight $2$
Character orbit 1840.i
Rep. character $\chi_{1840}(1471,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $3$
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.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(576\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 300 48 252
Cusp forms 276 48 228
Eisenstein series 24 0 24

Trace form

\( 48q - 48q^{9} + O(q^{10}) \) \( 48q - 48q^{9} - 48q^{25} + 24q^{29} - 24q^{41} + 24q^{49} + 60q^{69} - 96q^{77} + 72q^{81} + 96q^{93} + O(q^{100}) \)

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.i.a \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{3}-\beta _{10})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1840.2.i.b \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{13}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1840.2.i.c \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{5}q^{5}+(-\beta _{10}+\beta _{14})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)