Properties

Label 2268.2.i
Level $2268$
Weight $2$
Character orbit 2268.i
Rep. character $\chi_{2268}(865,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $14$
Sturm bound $864$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(13\), \(19\)

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

\( 64q - 5q^{7} + O(q^{10}) \) \( 64q - 5q^{7} + 5q^{13} - 10q^{19} - 32q^{25} + 20q^{31} + 5q^{37} - 10q^{43} - 17q^{49} + 60q^{55} - 22q^{61} + 2q^{67} + 2q^{73} + 26q^{79} + 12q^{85} + 11q^{91} + 5q^{97} + O(q^{100}) \)

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.i.a \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-1\) \(q+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
2268.2.i.b \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(4\) \(q+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
2268.2.i.c \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+(-3+2\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.i.d \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+(-2+3\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots\)
2268.2.i.e \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(q+(1-3\zeta_{6})q^{7}+7\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.i.f \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(q+(3-\zeta_{6})q^{7}-5\zeta_{6}q^{13}-8\zeta_{6}q^{19}+\cdots\)
2268.2.i.g \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(4\) \(q+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
2268.2.i.h \(2\) \(18.110\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
2268.2.i.i \(4\) \(18.110\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(0\) \(0\) \(0\) \(-10\) \(q+\beta _{1}q^{5}+(-2+\beta _{2})q^{7}+(-2\beta _{1}-2\beta _{3})q^{11}+\cdots\)
2268.2.i.j \(6\) \(18.110\) 6.0.309123.1 None \(0\) \(0\) \(-1\) \(2\) \(q+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2268.2.i.k \(6\) \(18.110\) 6.0.309123.1 None \(0\) \(0\) \(1\) \(2\) \(q+(-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2268.2.i.l \(8\) \(18.110\) 8.0.310217769.2 None \(0\) \(0\) \(-2\) \(1\) \(q+(\beta _{1}+\beta _{2})q^{5}+\beta _{5}q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2268.2.i.m \(8\) \(18.110\) 8.0.310217769.2 None \(0\) \(0\) \(2\) \(1\) \(q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{5}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
2268.2.i.n \(16\) \(18.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) \(q-\beta _{13}q^{5}+\beta _{3}q^{7}-\beta _{12}q^{11}+(2-2\beta _{4}+\cdots)q^{13}+\cdots\)

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

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