Properties

Label 3840.1.c
Level $3840$
Weight $1$
Character orbit 3840.c
Rep. character $\chi_{3840}(3329,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $8$
Sturm bound $768$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3840.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(768\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3840, [\chi])\).

Total New Old
Modular forms 88 20 68
Cusp forms 40 12 28
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 4 q^{9} - 4 q^{25} - 4 q^{49} + 12 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3840.1.c.a 3840.c 15.d $1$ $1.916$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) 120.1.i.a \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{9}+q^{15}+q^{25}-q^{27}+\cdots\)
3840.1.c.b 3840.c 15.d $1$ $1.916$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) 120.1.i.a \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}+q^{5}+q^{9}-q^{15}+q^{25}-q^{27}+\cdots\)
3840.1.c.c 3840.c 15.d $1$ $1.916$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) 120.1.i.a \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}+q^{9}-q^{15}+q^{25}+q^{27}+\cdots\)
3840.1.c.d 3840.c 15.d $1$ $1.916$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) 120.1.i.a \(0\) \(1\) \(1\) \(0\) \(q+q^{3}+q^{5}+q^{9}+q^{15}+q^{25}+q^{27}+\cdots\)
3840.1.c.e 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{30}) \) 1920.1.i.e \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-i q^{5}+2 i q^{7}+q^{9}+i q^{15}+\cdots\)
3840.1.c.f 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{6}) \) 1920.1.i.a \(0\) \(0\) \(0\) \(0\) \(q-i q^{3}-i q^{5}-q^{9}-q^{15}-2 q^{23}+\cdots\)
3840.1.c.g 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{6}) \) 1920.1.i.a \(0\) \(0\) \(0\) \(0\) \(q+i q^{3}-i q^{5}-q^{9}+q^{15}+2 q^{23}+\cdots\)
3840.1.c.h 3840.c 15.d $2$ $1.916$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{30}) \) 1920.1.i.e \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-i q^{5}-2 i q^{7}+q^{9}-i q^{15}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3840, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)