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Properties

Label 1863.2.c
Level $1863$
Weight $2$
Character orbit 1863.c
Rep. character $\chi_{1863}(1862,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $3$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1863 = 3^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1863.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(432\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1863, [\chi])\).

Total New Old
Modular forms 228 100 128
Cusp forms 204 92 112
Eisenstein series 24 8 16

Trace form

\( 92 q - 84 q^{4} + O(q^{10}) \) \( 92 q - 84 q^{4} + 4 q^{13} + 100 q^{16} + 92 q^{25} + 16 q^{31} + 28 q^{46} - 64 q^{49} - 54 q^{52} + 24 q^{55} + 26 q^{58} - 70 q^{64} - 96 q^{70} + 16 q^{73} - 34 q^{82} - 22 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1863, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1863.2.c.a 1863.c 69.c $12$ $14.876$ 12.0.\(\cdots\).2 \(\Q(\sqrt{-23}) \) 207.2.g.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{4}q^{2}+(-2+\beta _{5})q^{4}+(\beta _{1}-2\beta _{4}+\cdots)q^{8}+\cdots\)
1863.2.c.b 1863.c 69.c $32$ $14.876$ None 207.2.g.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1863.2.c.c 1863.c 69.c $48$ $14.876$ None 1863.2.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1863, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1863, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(621, [\chi])\)\(^{\oplus 2}\)