Properties

Label 756.2.f
Level $756$
Weight $2$
Character orbit 756.f
Rep. character $\chi_{756}(377,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $4$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 162 10 152
Cusp forms 126 10 116
Eisenstein series 36 0 36

Trace form

\( 10q - q^{7} + O(q^{10}) \) \( 10q - q^{7} - 2q^{25} + 10q^{37} + 52q^{43} - 5q^{49} - 10q^{67} + 50q^{79} - 60q^{85} - 3q^{91} + O(q^{100}) \)

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.f.a \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-6\) \(4\) \(q-3q^{5}+(2-\zeta_{6})q^{7}+3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
756.2.f.b \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(q+(-2-\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(5+\cdots)q^{19}+\cdots\)
756.2.f.c \(2\) \(6.037\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(4\) \(q+3q^{5}+(2-\zeta_{6})q^{7}-3\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
756.2.f.d \(4\) \(6.037\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)