Properties

Label 3840.2.k
Level $3840$
Weight $2$
Character orbit 3840.k
Rep. character $\chi_{3840}(1921,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $30$
Sturm bound $1536$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(1536\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(23\), \(31\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

Total New Old
Modular forms 816 64 752
Cusp forms 720 64 656
Eisenstein series 96 0 96

Trace form

\( 64q - 64q^{9} + O(q^{10}) \) \( 64q - 64q^{9} - 64q^{25} + 128q^{49} - 64q^{57} - 64q^{73} + 64q^{81} + 64q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3840.2.k.a \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{3}-iq^{5}-4q^{7}-q^{9}+6iq^{13}+\cdots\)
3840.2.k.b \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+2iq^{11}+\cdots\)
3840.2.k.c \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{3}-iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\)
3840.2.k.d \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-iq^{3}+iq^{5}-4q^{7}-q^{9}+2iq^{13}+\cdots\)
3840.2.k.e \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-iq^{5}-4q^{7}-q^{9}+6iq^{11}+\cdots\)
3840.2.k.f \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}-iq^{5}-4q^{7}-q^{9}-2iq^{13}+\cdots\)
3840.2.k.g \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{11}+\cdots\)
3840.2.k.h \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}+iq^{5}-2q^{7}-q^{9}-6iq^{11}+\cdots\)
3840.2.k.i \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{11}+\cdots\)
3840.2.k.j \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}-4iq^{11}+6iq^{13}+\cdots\)
3840.2.k.k \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{5}-q^{9}-4iq^{11}+2iq^{13}+\cdots\)
3840.2.k.l \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}-2iq^{11}+4iq^{13}+\cdots\)
3840.2.k.m \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots\)
3840.2.k.n \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}+2iq^{13}-q^{15}+\cdots\)
3840.2.k.o \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}+4iq^{11}+6iq^{13}+\cdots\)
3840.2.k.p \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-q^{9}+4iq^{11}+2iq^{13}+\cdots\)
3840.2.k.q \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}+2iq^{11}+4iq^{13}+\cdots\)
3840.2.k.r \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots\)
3840.2.k.s \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-q^{9}-2iq^{13}+q^{15}+\cdots\)
3840.2.k.t \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q-iq^{3}-iq^{5}+2q^{7}-q^{9}+2iq^{11}+\cdots\)
3840.2.k.u \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}-iq^{5}+2q^{7}-q^{9}+2iq^{11}+\cdots\)
3840.2.k.v \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}-iq^{5}+2q^{7}-q^{9}-6iq^{11}+\cdots\)
3840.2.k.w \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+iq^{5}+4q^{7}-q^{9}+2iq^{13}+\cdots\)
3840.2.k.x \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}+iq^{5}+4q^{7}-q^{9}+6iq^{11}+\cdots\)
3840.2.k.y \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}-iq^{5}+4q^{7}-q^{9}-2iq^{13}+\cdots\)
3840.2.k.z \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+iq^{5}+4q^{7}-q^{9}-6iq^{13}+\cdots\)
3840.2.k.ba \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+iq^{5}+4q^{7}-q^{9}-2iq^{11}+\cdots\)
3840.2.k.bb \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+iq^{5}+4q^{7}-q^{9}-4iq^{11}+\cdots\)
3840.2.k.bc \(4\) \(30.663\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{3}+\beta _{1}q^{5}+(-1+\beta _{3})q^{7}-q^{9}+\cdots\)
3840.2.k.bd \(4\) \(30.663\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{3}-\beta _{1}q^{5}+(1-\beta _{3})q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)