Properties

Label 756.2.i
Level $756$
Weight $2$
Character orbit 756.i
Rep. character $\chi_{756}(37,\cdot)$
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.i (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

\( 16q + 4q^{5} + q^{7} + O(q^{10}) \) \( 16q + 4q^{5} + q^{7} + 2q^{11} - q^{13} + 5q^{17} + 2q^{19} - 7q^{23} - 8q^{25} - 2q^{29} - 4q^{31} + 11q^{35} - q^{37} + 24q^{41} + 2q^{43} - 12q^{47} + 7q^{49} + 18q^{53} - 12q^{55} - 14q^{59} + 26q^{61} + 18q^{65} + 14q^{67} + 14q^{71} + 14q^{73} + 43q^{77} + 2q^{79} + 26q^{83} - 6q^{85} + 21q^{89} + 5q^{91} - 76q^{95} - q^{97} + O(q^{100}) \)

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.i.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-5\) \(q+(2-2\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+4\zeta_{6}q^{11}+\cdots\)
756.2.i.b \(14\) \(6.037\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(6\) \(q-\beta _{3}q^{5}+(\beta _{5}+\beta _{12})q^{7}+\beta _{13}q^{11}+\cdots\)

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

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