Properties

Label 4608.2.d
Level $4608$
Weight $2$
Character orbit 4608.d
Rep. character $\chi_{4608}(2305,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $18$
Sturm bound $1536$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 4608 = 2^{9} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4608.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(1536\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\), \(23\)

Dimensions

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

Total New Old
Modular forms 832 80 752
Cusp forms 704 80 624
Eisenstein series 128 0 128

Trace form

\( 80q + O(q^{10}) \) \( 80q - 80q^{25} + 80q^{49} - 32q^{65} + 32q^{73} + 32q^{89} + O(q^{100}) \)

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.d.a \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+2\beta q^{5}-4q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
4608.2.d.b \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(8\) \(q+2\beta q^{5}+4q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
4608.2.d.c \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2-\zeta_{8}^{3})q^{7}+\zeta_{8}q^{11}+\cdots\)
4608.2.d.d \(4\) \(36.795\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{3}q^{7}-\beta _{1}q^{11}+\beta _{2}q^{13}+\cdots\)
4608.2.d.e \(4\) \(36.795\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}+2\beta _{2}q^{13}+\cdots\)
4608.2.d.f \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+(\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
4608.2.d.g \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2q^{17}+\cdots\)
4608.2.d.h \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}-\zeta_{8}^{3}q^{7}+(-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
4608.2.d.i \(4\) \(36.795\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots\)
4608.2.d.j \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}+3\zeta_{8}^{2}q^{11}+3\zeta_{8}q^{13}+\cdots\)
4608.2.d.k \(4\) \(36.795\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{11}-\zeta_{8}^{3}q^{17}+(-2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{19}+\cdots\)
4608.2.d.l \(4\) \(36.795\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+\beta _{3}q^{13}+\cdots\)
4608.2.d.m \(4\) \(36.795\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-2\beta _{2}q^{13}+\cdots\)
4608.2.d.n \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}-3\zeta_{8}^{3}q^{7}+3\zeta_{8}q^{11}+4\zeta_{8}^{2}q^{13}+\cdots\)
4608.2.d.o \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(2+\zeta_{8}^{3})q^{7}-\zeta_{8}q^{11}+\cdots\)
4608.2.d.p \(8\) \(36.795\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{5}-\beta _{2}q^{7}+(-\beta _{4}+\beta _{6})q^{11}+\cdots\)
4608.2.d.q \(8\) \(36.795\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{5}-\zeta_{24}^{3}q^{7}+\zeta_{24}q^{11}+\cdots\)
4608.2.d.r \(8\) \(36.795\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{5}+\zeta_{24}^{7}q^{7}-\zeta_{24}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)