Properties

Label 2304.3.h
Level $2304$
Weight $3$
Character orbit 2304.h
Rep. character $\chi_{2304}(2177,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $12$
Sturm bound $1152$
Trace bound $25$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2304.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1152\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2304, [\chi])\).

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

Trace form

\( 64q + O(q^{10}) \) \( 64q + 320q^{25} + 320q^{49} - 640q^{73} - 896q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2304.3.h.a \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-48\) \(q-5\zeta_{8}^{3}q^{5}-12q^{7}+4\zeta_{8}^{3}q^{11}-4\zeta_{8}q^{13}+\cdots\)
2304.3.h.b \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-32\) \(q+\zeta_{8}^{3}q^{5}-8q^{7}+8\zeta_{8}^{3}q^{11}-4\zeta_{8}q^{13}+\cdots\)
2304.3.h.c \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-16\) \(q+\zeta_{8}^{3}q^{5}-4q^{7}+4\zeta_{8}^{3}q^{11}+4\zeta_{8}q^{13}+\cdots\)
2304.3.h.d \(4\) \(62.779\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{5}+12\zeta_{8}q^{13}+23\zeta_{8}^{2}q^{17}+\cdots\)
2304.3.h.e \(4\) \(62.779\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-7\zeta_{8}^{3}q^{5}+12\zeta_{8}q^{13}-7\zeta_{8}^{2}q^{17}+\cdots\)
2304.3.h.f \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(16\) \(q+\zeta_{8}^{3}q^{5}+4q^{7}-4\zeta_{8}^{3}q^{11}+4\zeta_{8}q^{13}+\cdots\)
2304.3.h.g \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(32\) \(q+\zeta_{8}^{3}q^{5}+8q^{7}-8\zeta_{8}^{3}q^{11}+4\zeta_{8}q^{13}+\cdots\)
2304.3.h.h \(4\) \(62.779\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(48\) \(q+5\zeta_{8}^{3}q^{5}+12q^{7}+4\zeta_{8}^{3}q^{11}-4\zeta_{8}q^{13}+\cdots\)
2304.3.h.i \(8\) \(62.779\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-16\) \(q+(\zeta_{24}^{3}+\zeta_{24}^{5})q^{5}+(-2+\zeta_{24}^{7})q^{7}+\cdots\)
2304.3.h.j \(8\) \(62.779\) 8.0.959512576.1 None \(0\) \(0\) \(0\) \(-16\) \(q+(\beta _{3}-\beta _{5})q^{5}-2q^{7}+(-4\beta _{3}+2\beta _{5}+\cdots)q^{11}+\cdots\)
2304.3.h.k \(8\) \(62.779\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(16\) \(q+(\zeta_{24}^{3}+\zeta_{24}^{5})q^{5}+(2-\zeta_{24}^{7})q^{7}+\cdots\)
2304.3.h.l \(8\) \(62.779\) 8.0.959512576.1 None \(0\) \(0\) \(0\) \(16\) \(q+(-\beta _{3}+\beta _{5})q^{5}+2q^{7}+(-4\beta _{3}+2\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)