Properties

Label 4368.2.h
Level $4368$
Weight $2$
Character orbit 4368.h
Rep. character $\chi_{4368}(337,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $20$
Sturm bound $1792$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4368.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(1792\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4368, [\chi])\).

Total New Old
Modular forms 920 84 836
Cusp forms 872 84 788
Eisenstein series 48 0 48

Trace form

\( 84 q + 84 q^{9} + O(q^{10}) \) \( 84 q + 84 q^{9} - 4 q^{13} + 8 q^{17} - 92 q^{25} - 8 q^{29} - 40 q^{43} - 84 q^{49} - 24 q^{51} + 8 q^{53} - 32 q^{55} + 8 q^{61} + 16 q^{65} - 16 q^{75} - 88 q^{79} + 84 q^{81} + 48 q^{87} + 104 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4368.2.h.a 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+4iq^{5}-iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots\)
4368.2.h.b 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+3iq^{5}+iq^{7}+q^{9}-5iq^{11}+\cdots\)
4368.2.h.c 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{7}+q^{9}+4iq^{11}+(-3+\cdots)q^{13}+\cdots\)
4368.2.h.d 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+iq^{7}+q^{9}+(2+3i)q^{13}+\cdots\)
4368.2.h.e 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+3iq^{5}+iq^{7}+q^{9}+(2-3i)q^{13}+\cdots\)
4368.2.h.f 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2iq^{5}-iq^{7}+q^{9}+(2+3i)q^{13}+\cdots\)
4368.2.h.g 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+3iq^{5}-iq^{7}+q^{9}+4iq^{11}+\cdots\)
4368.2.h.h 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-iq^{7}+q^{9}+3iq^{11}+\cdots\)
4368.2.h.i 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+3iq^{5}-iq^{7}+q^{9}-5iq^{11}+\cdots\)
4368.2.h.j 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
4368.2.h.k 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
4368.2.h.l 4368.h 13.b $4$ $34.879$ \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
4368.2.h.m 4368.h 13.b $4$ $34.879$ \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{2}q^{5}-\beta _{2}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
4368.2.h.n 4368.h 13.b $4$ $34.879$ \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
4368.2.h.o 4368.h 13.b $6$ $34.879$ 6.0.350464.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{5}+\beta _{4}q^{7}+\cdots\)
4368.2.h.p 4368.h 13.b $6$ $34.879$ 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
4368.2.h.q 4368.h 13.b $8$ $34.879$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(\beta _{2}-\beta _{7})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
4368.2.h.r 4368.h 13.b $10$ $34.879$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+q^{9}+(\beta _{3}-\beta _{9})q^{11}+\cdots\)
4368.2.h.s 4368.h 13.b $10$ $34.879$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-\beta _{1}-\beta _{6})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
4368.2.h.t 4368.h 13.b $10$ $34.879$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(\beta _{1}+\beta _{5})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1092, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2184, [\chi])\)\(^{\oplus 2}\)