Properties

Label 2268.2.t
Level $2268$
Weight $2$
Character orbit 2268.t
Rep. character $\chi_{2268}(1781,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $3$
Sturm bound $864$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(864\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

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

\( 64 q - 4 q^{7} + O(q^{10}) \) \( 64 q - 4 q^{7} - 32 q^{25} + 12 q^{31} - 2 q^{37} + 16 q^{43} - 20 q^{49} + 6 q^{61} - 10 q^{67} - 36 q^{73} + 26 q^{79} - 48 q^{85} - 18 q^{91} + O(q^{100}) \)

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.t.a \(16\) \(18.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{9}q^{5}+\beta _{3}q^{7}+\beta _{15}q^{11}+\beta _{1}q^{13}+\cdots\)
2268.2.t.b \(16\) \(18.110\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{11}q^{5}-\beta _{4}q^{7}+(-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
2268.2.t.c \(32\) \(18.110\) None \(0\) \(0\) \(0\) \(-8\)

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

\( S_{2}^{\mathrm{old}}(2268, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1134, [\chi])\)\(^{\oplus 2}\)