Properties

Label 2304.2.k
Level $2304$
Weight $2$
Character orbit 2304.k
Rep. character $\chi_{2304}(577,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
Newform subspaces $12$
Sturm bound $768$
Trace bound $37$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 12 \)
Sturm bound: \(768\)
Trace bound: \(37\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

Total New Old
Modular forms 864 80 784
Cusp forms 672 80 592
Eisenstein series 192 0 192

Trace form

\( 80q + O(q^{10}) \) \( 80q - 80q^{49} - 96q^{65} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2304.2.k.a \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-2+2\zeta_{8})q^{5}-3\zeta_{8}^{2}q^{7}+(2\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
2304.2.k.b \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{7}+(-1+\zeta_{8})q^{13}-6q^{17}+\cdots\)
2304.2.k.c \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+(1-\zeta_{8})q^{13}-6q^{17}+(-3\zeta_{8}^{2}+\cdots)q^{19}+\cdots\)
2304.2.k.d \(4\) \(18.398\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) \(q+(2-2\zeta_{8})q^{5}+3\zeta_{8}^{2}q^{7}+(2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{11}+\cdots\)
2304.2.k.e \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1+\zeta_{24}^{2}-\zeta_{24}^{7})q^{5}-\zeta_{24}^{4}q^{7}+\cdots\)
2304.2.k.f \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{5}-\zeta_{24}^{3}q^{7}+(\zeta_{24}+\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
2304.2.k.g \(8\) \(18.398\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{7}+(-1+\zeta_{24}^{2}+\zeta_{24}^{7})q^{13}+\cdots\)
2304.2.k.h \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{5}-\zeta_{24}^{2}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)
2304.2.k.i \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{5}-\zeta_{24}^{2}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)
2304.2.k.j \(8\) \(18.398\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{7}+(1-\zeta_{24}^{2}-\zeta_{24}^{7})q^{13}+\cdots\)
2304.2.k.k \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{6}q^{5}+(\zeta_{24}-\zeta_{24}^{5})q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
2304.2.k.l \(8\) \(18.398\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) \(q+(1-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}-\zeta_{24}^{4}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)