Properties

Label 768.2.d
Level $768$
Weight $2$
Character orbit 768.d
Rep. character $\chi_{768}(385,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $8$
Sturm bound $256$
Trace bound $15$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(256\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(5\), \(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(768, [\chi])\).

Total New Old
Modular forms 152 16 136
Cusp forms 104 16 88
Eisenstein series 48 0 48

Trace form

\( 16q - 16q^{9} + O(q^{10}) \) \( 16q - 16q^{9} - 16q^{25} - 16q^{49} + 32q^{57} - 32q^{65} + 64q^{73} + 16q^{81} + 32q^{89} - 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(768, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
768.2.d.a \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}+2iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\)
768.2.d.b \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}-2q^{7}-q^{9}-4iq^{11}-6iq^{13}+\cdots\)
768.2.d.c \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-iq^{3}+4iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots\)
768.2.d.d \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{5}-q^{9}+4iq^{11}-2iq^{13}+\cdots\)
768.2.d.e \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{5}-q^{9}-4iq^{11}-2iq^{13}+\cdots\)
768.2.d.f \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}+4iq^{5}+2q^{7}-q^{9}+4iq^{11}+\cdots\)
768.2.d.g \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q-iq^{3}+2q^{7}-q^{9}+4iq^{11}-6iq^{13}+\cdots\)
768.2.d.h \(2\) \(6.133\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q-iq^{3}+2iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(768, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(768, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)