Properties

Label 4608.2.k
Level $4608$
Weight $2$
Character orbit 4608.k
Rep. character $\chi_{4608}(1153,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Newform subspaces $38$
Sturm bound $1536$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 4608 = 2^{9} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4608.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 38 \)
Sturm bound: \(1536\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4608, [\chi])\).

Total New Old
Modular forms 1664 160 1504
Cusp forms 1408 160 1248
Eisenstein series 256 0 256

Trace form

\( 160q + O(q^{10}) \) \( 160q - 160q^{49} + 64q^{65} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4608, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4608.2.k.a \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q+(-3-3i)q^{5}+(-5+5i)q^{13}-2q^{17}+\cdots\)
4608.2.k.b \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q+(-3-3i)q^{5}+(1-i)q^{13}+8q^{17}+\cdots\)
4608.2.k.c \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q+(-3-3i)q^{5}+(5-5i)q^{13}+2q^{17}+\cdots\)
4608.2.k.d \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-4iq^{7}+(-4-4i)q^{11}+\cdots\)
4608.2.k.e \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-4iq^{7}+(-4-4i)q^{11}+\cdots\)
4608.2.k.f \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+4iq^{7}+(-2-2i)q^{11}+\cdots\)
4608.2.k.g \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+(-5+5i)q^{13}-8q^{17}+\cdots\)
4608.2.k.h \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+(-1+i)q^{13}+2q^{17}+\cdots\)
4608.2.k.i \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+(1-i)q^{13}-2q^{17}+\cdots\)
4608.2.k.j \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-4iq^{7}+(2+2i)q^{11}+\cdots\)
4608.2.k.k \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+4iq^{7}+(4+4i)q^{11}+\cdots\)
4608.2.k.l \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+4iq^{7}+(4+4i)q^{11}+\cdots\)
4608.2.k.m \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+4iq^{7}+(-4-4i)q^{11}+\cdots\)
4608.2.k.n \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+4iq^{7}+(-4-4i)q^{11}+\cdots\)
4608.2.k.o \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-4iq^{7}+(-2-2i)q^{11}+\cdots\)
4608.2.k.p \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+(-1+i)q^{13}-2q^{17}+\cdots\)
4608.2.k.q \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+(1-i)q^{13}+2q^{17}-3iq^{25}+\cdots\)
4608.2.k.r \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+(5-5i)q^{13}-8q^{17}+\cdots\)
4608.2.k.s \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+4iq^{7}+(2+2i)q^{11}+\cdots\)
4608.2.k.t \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-4iq^{7}+(4+4i)q^{11}+\cdots\)
4608.2.k.u \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-4iq^{7}+(4+4i)q^{11}+\cdots\)
4608.2.k.v \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+(3+3i)q^{5}+(-5+5i)q^{13}+2q^{17}+\cdots\)
4608.2.k.w \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+(3+3i)q^{5}+(-1+i)q^{13}+8q^{17}+\cdots\)
4608.2.k.x \(2\) \(36.795\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+(3+3i)q^{5}+(5-5i)q^{13}-2q^{17}+\cdots\)
4608.2.k.y \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-1+\zeta_{8})q^{5}+\zeta_{8}^{2}q^{7}+(-3-3\zeta_{8}+\cdots)q^{13}+\cdots\)
4608.2.k.z \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{5}-\zeta_{8}q^{11}+(-1+\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
4608.2.k.ba \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) \(q+(1+\zeta_{8}^{2})q^{5}-\zeta_{8}q^{11}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
4608.2.k.bb \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) \(q+(1-\zeta_{8})q^{5}+\zeta_{8}^{2}q^{7}+(3+3\zeta_{8})q^{13}+\cdots\)
4608.2.k.bc \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1-\zeta_{16}^{3}+\zeta_{16}^{7})q^{5}+(\zeta_{16}^{2}+\cdots)q^{7}+\cdots\)
4608.2.k.bd \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1+\zeta_{16}-\zeta_{16}^{2})q^{5}-\zeta_{16}^{3}q^{7}+\cdots\)
4608.2.k.be \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1-\zeta_{16}^{3}+\zeta_{16}^{7})q^{5}+(-\zeta_{16}^{2}+\cdots)q^{7}+\cdots\)
4608.2.k.bf \(8\) \(36.795\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{5}+\beta _{3}q^{7}+(\beta _{2}+\beta _{3}+\beta _{4})q^{11}+\cdots\)
4608.2.k.bg \(8\) \(36.795\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{5}-\beta _{3}q^{7}+(\beta _{2}+\beta _{3}+\beta _{4})q^{11}+\cdots\)
4608.2.k.bh \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) \(q+(1-\zeta_{16}^{2}-\zeta_{16}^{3}+\zeta_{16}^{5})q^{5}+(-\zeta_{16}^{2}+\cdots)q^{7}+\cdots\)
4608.2.k.bi \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) \(q+(1-\zeta_{16}^{2}+\zeta_{16}^{4})q^{5}-\zeta_{16}^{3}q^{7}+\cdots\)
4608.2.k.bj \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) \(q+(1-\zeta_{16}^{2}-\zeta_{16}^{3}+\zeta_{16}^{5})q^{5}+(\zeta_{16}^{2}+\cdots)q^{7}+\cdots\)
4608.2.k.bk \(16\) \(36.795\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{14}q^{7}-\beta _{1}q^{11}+(-1+\cdots)q^{13}+\cdots\)
4608.2.k.bl \(16\) \(36.795\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{14}q^{7}-\beta _{1}q^{11}+(1-\beta _{5}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4608, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)