Properties

Label 3072.2.d
Level $3072$
Weight $2$
Character orbit 3072.d
Rep. character $\chi_{3072}(1537,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $10$
Sturm bound $1024$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3072.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(1024\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).

Total New Old
Modular forms 560 64 496
Cusp forms 464 64 400
Eisenstein series 96 0 96

Trace form

\( 64q - 64q^{9} + O(q^{10}) \) \( 64q - 64q^{9} - 64q^{25} + 64q^{49} + 64q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3072.2.d.a \(4\) \(24.530\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}-q^{9}-\zeta_{8}^{2}q^{13}+\cdots\)
3072.2.d.b \(4\) \(24.530\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-q^{9}+4\zeta_{8}q^{11}+\cdots\)
3072.2.d.c \(4\) \(24.530\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3072.2.d.d \(4\) \(24.530\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{5}+3\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3072.2.d.e \(8\) \(24.530\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-16\) \(q+\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3072.2.d.f \(8\) \(24.530\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
3072.2.d.g \(8\) \(24.530\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}-\beta _{7})q^{7}-q^{9}+\cdots\)
3072.2.d.h \(8\) \(24.530\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{3}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{5}+\zeta_{24}^{3}q^{7}+\cdots\)
3072.2.d.i \(8\) \(24.530\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
3072.2.d.j \(8\) \(24.530\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(16\) \(q-\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(2-\zeta_{16}^{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1024, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)