Properties

Label 2312.1.p
Level $2312$
Weight $1$
Character orbit 2312.p
Rep. character $\chi_{2312}(155,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $24$
Newform subspaces $5$
Sturm bound $306$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2312 = 2^{3} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2312.p (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 5 \)
Sturm bound: \(306\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2312, [\chi])\).

Total New Old
Modular forms 104 80 24
Cusp forms 32 24 8
Eisenstein series 72 56 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q + 4 q^{9} + 4 q^{11} - 4 q^{12} - 24 q^{16} - 8 q^{18} - 4 q^{24} - 4 q^{27} + 16 q^{33} + 4 q^{36} - 4 q^{43} - 4 q^{54} + 4 q^{59} - 4 q^{66} + 8 q^{67} + 4 q^{75} + 4 q^{82} - 4 q^{83} - 8 q^{86}+ \cdots + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(2312, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2312.1.p.a 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-2}) \) None 136.1.p.a \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(-1-\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2312.1.p.b 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-2}) \) None 136.1.p.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2312.1.p.c 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) $D_{2}$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) 136.1.e.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
2312.1.p.d 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) $D_{8}$ \(\Q(\sqrt{-2}) \) None 136.1.p.a \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
2312.1.p.e 2312.p 136.p $8$ $1.154$ \(\Q(\zeta_{16})\) $D_{4}$ \(\Q(\sqrt{-2}) \) None 136.1.j.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{2}+(-\zeta_{16}^{3}-\zeta_{16}^{7})q^{3}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2312, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2312, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)