Properties

Label 3264.2.c
Level $3264$
Weight $2$
Character orbit 3264.c
Rep. character $\chi_{3264}(577,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $18$
Sturm bound $1152$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3264.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(1152\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(13\), \(19\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3264, [\chi])\).

Total New Old
Modular forms 600 72 528
Cusp forms 552 72 480
Eisenstein series 48 0 48

Trace form

\( 72q - 72q^{9} + O(q^{10}) \) \( 72q - 72q^{9} - 8q^{17} - 88q^{25} - 72q^{49} - 32q^{69} + 96q^{77} + 72q^{81} - 32q^{85} - 16q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3264, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3264.2.c.a \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{5}-2iq^{7}-q^{9}+3iq^{11}+\cdots\)
3264.2.c.b \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}+2iq^{7}-q^{9}-3iq^{11}+\cdots\)
3264.2.c.c \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{5}-2iq^{7}-q^{9}-2q^{13}+\cdots\)
3264.2.c.d \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-4iq^{7}-q^{9}-4iq^{11}-2q^{13}+\cdots\)
3264.2.c.e \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-4iq^{7}-q^{9}-4iq^{11}-2q^{13}+\cdots\)
3264.2.c.f \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{5}+2iq^{7}-q^{9}-2q^{13}+\cdots\)
3264.2.c.g \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{5}-2iq^{7}-q^{9}-5iq^{11}+\cdots\)
3264.2.c.h \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+3iq^{5}+2iq^{7}-q^{9}+5iq^{11}+\cdots\)
3264.2.c.i \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2iq^{5}-2iq^{7}-q^{9}+6q^{13}+\cdots\)
3264.2.c.j \(2\) \(26.063\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+2iq^{5}+2iq^{7}-q^{9}+6q^{13}+\cdots\)
3264.2.c.k \(4\) \(26.063\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots\)
3264.2.c.l \(4\) \(26.063\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+2\beta _{2}q^{7}-q^{9}+\cdots\)
3264.2.c.m \(4\) \(26.063\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}-4\beta _{1}q^{7}-q^{9}+3\beta _{1}q^{11}+\cdots\)
3264.2.c.n \(6\) \(26.063\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
3264.2.c.o \(6\) \(26.063\) 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
3264.2.c.p \(8\) \(26.063\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{3}q^{5}-q^{9}+(3\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots\)
3264.2.c.q \(10\) \(26.063\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}+\beta _{9}q^{5}+\beta _{3}q^{7}-q^{9}+(\beta _{6}+\cdots)q^{11}+\cdots\)
3264.2.c.r \(10\) \(26.063\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{9}q^{5}-\beta _{3}q^{7}-q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3264, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3264, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1088, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1632, [\chi])\)\(^{\oplus 2}\)