Properties

Label 2268.2.x
Level $2268$
Weight $2$
Character orbit 2268.x
Rep. character $\chi_{2268}(377,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $11$
Sturm bound $864$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 11 \)
Sturm bound: \(864\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2268, [\chi])\).

Total New Old
Modular forms 936 64 872
Cusp forms 792 64 728
Eisenstein series 144 0 144

Trace form

\( 64q + 5q^{7} + O(q^{10}) \) \( 64q + 5q^{7} - 32q^{25} - 20q^{37} - 20q^{43} + 7q^{49} + 2q^{67} - 82q^{79} - 12q^{85} + 18q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2268, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2268.2.x.a \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-5\) \(q-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+\cdots\)
2268.2.x.b \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(1\) \(q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(3+3\zeta_{6})q^{11}+\cdots\)
2268.2.x.c \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(q+(-3+\zeta_{6})q^{7}+(-8+4\zeta_{6})q^{13}+\cdots\)
2268.2.x.d \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+(2-3\zeta_{6})q^{7}+(2-\zeta_{6})q^{13}+(-5+\cdots)q^{19}+\cdots\)
2268.2.x.e \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+(-1+3\zeta_{6})q^{7}+(8-4\zeta_{6})q^{13}+(-2+\cdots)q^{19}+\cdots\)
2268.2.x.f \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q+(3-2\zeta_{6})q^{7}+(-2+\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots\)
2268.2.x.g \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-5\) \(q+3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(3+3\zeta_{6})q^{11}+\cdots\)
2268.2.x.h \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-3-3\zeta_{6})q^{11}+\cdots\)
2268.2.x.i \(8\) \(18.110\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{24}^{2}q^{5}+(1-\zeta_{24}+\zeta_{24}^{5})q^{7}+\cdots\)
2268.2.x.j \(8\) \(18.110\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) \(q+(-\zeta_{24}^{2}+\zeta_{24}^{4})q^{5}+(\zeta_{24}-\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
2268.2.x.k \(32\) \(18.110\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(2268, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)