Properties

Label 3822.2.c
Level $3822$
Weight $2$
Character orbit 3822.c
Rep. character $\chi_{3822}(883,\cdot)$
Character field $\Q$
Dimension $98$
Newform subspaces $16$
Sturm bound $1568$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(1568\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3822, [\chi])\).

Total New Old
Modular forms 816 98 718
Cusp forms 752 98 654
Eisenstein series 64 0 64

Trace form

\( 98 q - 2 q^{3} - 98 q^{4} + 98 q^{9} + O(q^{10}) \) \( 98 q - 2 q^{3} - 98 q^{4} + 98 q^{9} + 4 q^{10} + 2 q^{12} - 10 q^{13} + 98 q^{16} - 12 q^{17} + 8 q^{22} - 8 q^{23} - 126 q^{25} - 4 q^{26} - 2 q^{27} + 4 q^{29} - 4 q^{30} - 98 q^{36} + 4 q^{38} - 14 q^{39} - 4 q^{40} - 56 q^{43} - 2 q^{48} - 4 q^{51} + 10 q^{52} + 60 q^{53} + 64 q^{55} - 20 q^{61} + 20 q^{62} - 98 q^{64} + 72 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{69} - 48 q^{74} - 2 q^{75} - 4 q^{78} + 48 q^{79} + 98 q^{81} + 28 q^{82} + 28 q^{87} - 8 q^{88} + 4 q^{90} + 8 q^{92} - 16 q^{94} - 72 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3822, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3822.2.c.a 3822.c 13.b $2$ $30.519$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}+3iq^{5}-iq^{6}+\cdots\)
3822.2.c.b 3822.c 13.b $2$ $30.519$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-iq^{8}+\cdots\)
3822.2.c.c 3822.c 13.b $2$ $30.519$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
3822.2.c.d 3822.c 13.b $2$ $30.519$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
3822.2.c.e 3822.c 13.b $2$ $30.519$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}-iq^{8}+\cdots\)
3822.2.c.f 3822.c 13.b $4$ $30.519$ \(\Q(i, \sqrt{10})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
3822.2.c.g 3822.c 13.b $4$ $30.519$ \(\Q(i, \sqrt{10})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{3}-q^{4}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
3822.2.c.h 3822.c 13.b $4$ $30.519$ \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
3822.2.c.i 3822.c 13.b $6$ $30.519$ 6.0.3356224.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots\)
3822.2.c.j 3822.c 13.b $6$ $30.519$ 6.0.9144576.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
3822.2.c.k 3822.c 13.b $6$ $30.519$ 6.0.9144576.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
3822.2.c.l 3822.c 13.b $6$ $30.519$ 6.0.3356224.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}-q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots\)
3822.2.c.m 3822.c 13.b $10$ $30.519$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots\)
3822.2.c.n 3822.c 13.b $10$ $30.519$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots\)
3822.2.c.o 3822.c 13.b $16$ $30.519$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}-q^{3}-q^{4}-\beta _{4}q^{5}-\beta _{7}q^{6}+\cdots\)
3822.2.c.p 3822.c 13.b $16$ $30.519$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+q^{3}-q^{4}-\beta _{4}q^{5}-\beta _{7}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3822, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)