Properties

Label 756.2.l
Level $756$
Weight $2$
Character orbit 756.l
Rep. character $\chi_{756}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 324 16 308
Cusp forms 252 16 236
Eisenstein series 72 0 72

Trace form

\( 16q - 8q^{5} + q^{7} + O(q^{10}) \) \( 16q - 8q^{5} + q^{7} - 4q^{11} - q^{13} + 5q^{17} + 2q^{19} + 14q^{23} + 16q^{25} - 2q^{29} + 2q^{31} + 11q^{35} - q^{37} + 24q^{41} + 2q^{43} + 6q^{47} - 11q^{49} + 18q^{53} - 12q^{55} + 7q^{59} - 13q^{61} - 9q^{65} - 7q^{67} + 14q^{71} + 14q^{73} - 35q^{77} - q^{79} + 26q^{83} - 6q^{85} + 21q^{89} + 5q^{91} + 38q^{95} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
756.2.l.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(4\) \(q-2q^{5}+(3-2\zeta_{6})q^{7}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
756.2.l.b \(14\) \(6.037\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(-4\) \(-3\) \(q+(\beta _{3}-\beta _{7})q^{5}-\beta _{5}q^{7}+(\beta _{9}-\beta _{13})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

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