Properties

Label 1456.2.r
Level $1456$
Weight $2$
Character orbit 1456.r
Rep. character $\chi_{1456}(417,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $18$
Sturm bound $448$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 18 \)
Sturm bound: \(448\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

Total New Old
Modular forms 472 96 376
Cusp forms 424 96 328
Eisenstein series 48 0 48

Trace form

\( 96 q - 48 q^{9} + O(q^{10}) \) \( 96 q - 48 q^{9} + 4 q^{11} - 12 q^{19} + 8 q^{21} + 16 q^{23} - 56 q^{25} + 32 q^{29} + 12 q^{31} - 8 q^{33} + 36 q^{35} - 8 q^{37} - 8 q^{43} - 8 q^{45} + 8 q^{47} + 8 q^{49} - 20 q^{51} - 12 q^{53} - 24 q^{55} - 36 q^{59} - 4 q^{61} - 76 q^{63} + 8 q^{67} - 32 q^{69} - 8 q^{71} + 16 q^{73} + 36 q^{75} + 4 q^{77} + 20 q^{79} - 40 q^{81} + 88 q^{83} - 32 q^{85} + 36 q^{87} + 8 q^{89} + 16 q^{93} + 12 q^{95} - 16 q^{97} - 112 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1456.2.r.a \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(3\) \(4\) \(q+(-3+3\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.b \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-5\) \(q+(-2+2\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.r.c \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-4\) \(q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.d \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(4\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1456.2.r.e \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(4\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1456.2.r.f \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(1-\zeta_{6})q^{11}+\cdots\)
1456.2.r.g \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots\)
1456.2.r.h \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(-4\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.i \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(4\) \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1456.2.r.j \(4\) \(11.626\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(3+2\beta _{1})q^{7}+\cdots\)
1456.2.r.k \(4\) \(11.626\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(4\) \(0\) \(0\) \(q+(2+2\beta _{2})q^{3}+(\beta _{1}+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1456.2.r.l \(6\) \(11.626\) 6.0.309123.1 None \(0\) \(0\) \(2\) \(4\) \(q+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{5})q^{3}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
1456.2.r.m \(8\) \(11.626\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-1\) \(-1\) \(-1\) \(q+(\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
1456.2.r.n \(8\) \(11.626\) 8.0.8681953329.1 None \(0\) \(0\) \(-2\) \(-7\) \(q+(\beta _{1}+\beta _{7})q^{3}+(-\beta _{2}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
1456.2.r.o \(8\) \(11.626\) 8.0.856615824.2 None \(0\) \(3\) \(1\) \(-1\) \(q+(\beta _{1}-\beta _{2}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
1456.2.r.p \(10\) \(11.626\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-2\) \(-1\) \(q-\beta _{9}q^{3}+(-\beta _{3}-\beta _{7})q^{5}+(\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
1456.2.r.q \(14\) \(11.626\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-2\) \(-2\) \(2\) \(q-\beta _{1}q^{3}-\beta _{9}q^{5}+\beta _{4}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
1456.2.r.r \(16\) \(11.626\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(2\) \(0\) \(-1\) \(q+\beta _{1}q^{3}+(\beta _{4}+\beta _{10})q^{5}+(\beta _{5}-\beta _{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)