Properties

Label 1456.2.s
Level $1456$
Weight $2$
Character orbit 1456.s
Rep. character $\chi_{1456}(113,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $84$
Newform subspaces $19$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 472 84 388
Cusp forms 424 84 340
Eisenstein series 48 0 48

Trace form

\( 84 q + 4 q^{5} - 42 q^{9} + O(q^{10}) \) \( 84 q + 4 q^{5} - 42 q^{9} + 2 q^{13} + 2 q^{17} + 12 q^{23} + 80 q^{25} + 24 q^{27} - 2 q^{29} - 12 q^{35} - 10 q^{37} - 36 q^{39} + 2 q^{41} + 4 q^{43} - 10 q^{45} + 48 q^{47} - 42 q^{49} + 24 q^{51} + 4 q^{53} + 40 q^{55} + 16 q^{57} + 36 q^{59} - 10 q^{61} + 2 q^{65} + 24 q^{67} + 12 q^{71} - 20 q^{73} + 16 q^{75} - 64 q^{79} - 50 q^{81} + 40 q^{83} + 18 q^{85} + 12 q^{87} - 28 q^{89} - 48 q^{93} - 12 q^{97} - 152 q^{99} + O(q^{100}) \)

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.s.a \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-6\) \(1\) \(q+(-2+2\zeta_{6})q^{3}-3q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.s.b \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(-1\) \(q+(-2+2\zeta_{6})q^{3}+q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.s.c \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-1\) \(q-q^{5}-\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-2+2\zeta_{6})q^{11}+\cdots\)
1456.2.s.d \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(6\) \(1\) \(q+3q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-2+2\zeta_{6})q^{11}+\cdots\)
1456.2.s.e \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(1\) \(q+(1-\zeta_{6})q^{3}+3q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1456.2.s.f \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(2\) \(1\) \(q+(2-2\zeta_{6})q^{3}+q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1456.2.s.g \(2\) \(11.626\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-6\) \(1\) \(q+(3-3\zeta_{6})q^{3}-3q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1456.2.s.h \(4\) \(11.626\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(-3\) \(6\) \(2\) \(q+(-1-\beta _{1}-\beta _{3})q^{3}+(1-\beta _{2})q^{5}+\cdots\)
1456.2.s.i \(4\) \(11.626\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-2\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-\zeta_{12}^{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1456.2.s.j \(4\) \(11.626\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(8\) \(2\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}+\cdots)q^{5}+\cdots\)
1456.2.s.k \(4\) \(11.626\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(-1\) \(-6\) \(2\) \(q-\beta _{3}q^{3}+(-2+\beta _{2})q^{5}-\beta _{1}q^{7}+(2\beta _{1}+\cdots)q^{9}+\cdots\)
1456.2.s.l \(4\) \(11.626\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(8\) \(-2\) \(q-\zeta_{12}^{2}q^{3}+(2-\zeta_{12}^{3})q^{5}+(-1+\zeta_{12}+\cdots)q^{7}+\cdots\)
1456.2.s.m \(4\) \(11.626\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(1\) \(6\) \(-2\) \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1456.2.s.n \(4\) \(11.626\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(1\) \(10\) \(-2\) \(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1456.2.s.o \(4\) \(11.626\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(2\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{3}q^{5}+(1-\zeta_{12}+\cdots)q^{7}+\cdots\)
1456.2.s.p \(8\) \(11.626\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(-10\) \(4\) \(q+(\beta _{1}+\beta _{4})q^{3}+(-1-\beta _{6})q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
1456.2.s.q \(8\) \(11.626\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(-14\) \(-4\) \(q+(-\beta _{5}+\beta _{6})q^{3}+(-2-\beta _{3})q^{5}+\beta _{4}q^{7}+\cdots\)
1456.2.s.r \(8\) \(11.626\) 8.0.4277552409.3 None \(0\) \(3\) \(-10\) \(4\) \(q+(\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{7})q^{5}+\cdots\)
1456.2.s.s \(14\) \(11.626\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(1\) \(4\) \(-7\) \(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)