Properties

Label 3330.2.h
Level $3330$
Weight $2$
Character orbit 3330.h
Rep. character $\chi_{3330}(2071,\cdot)$
Character field $\Q$
Dimension $66$
Newform subspaces $16$
Sturm bound $1368$
Trace bound $26$

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Defining parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(1368\)
Trace bound: \(26\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3330, [\chi])\).

Total New Old
Modular forms 700 66 634
Cusp forms 668 66 602
Eisenstein series 32 0 32

Trace form

\( 66 q - 66 q^{4} + O(q^{10}) \) \( 66 q - 66 q^{4} + 2 q^{10} - 4 q^{11} + 66 q^{16} - 66 q^{25} - 4 q^{26} + 24 q^{34} + 4 q^{37} - 16 q^{38} - 2 q^{40} - 8 q^{41} + 4 q^{44} - 8 q^{46} - 8 q^{47} + 62 q^{49} - 16 q^{53} + 12 q^{58} + 52 q^{62} - 66 q^{64} + 4 q^{65} - 4 q^{67} + 4 q^{70} + 24 q^{71} + 28 q^{73} + 10 q^{74} + 20 q^{83} + 4 q^{85} - 36 q^{86} + 8 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3330, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3330.2.h.a 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{5}-4q^{7}+iq^{8}+\cdots\)
3330.2.h.b 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{5}-4q^{7}+iq^{8}+\cdots\)
3330.2.h.c 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}-2q^{7}-iq^{8}+\cdots\)
3330.2.h.d 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{5}-q^{7}+iq^{8}-q^{10}+\cdots\)
3330.2.h.e 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{5}+q^{7}+iq^{8}-q^{10}+\cdots\)
3330.2.h.f 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}+q^{7}-iq^{8}-q^{10}+\cdots\)
3330.2.h.g 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}-iq^{5}+q^{7}+iq^{8}-q^{10}+\cdots\)
3330.2.h.h 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}+2q^{7}-iq^{8}+\cdots\)
3330.2.h.i 3330.h 37.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}+5q^{7}-iq^{8}+\cdots\)
3330.2.h.j 3330.h 37.b $4$ $26.590$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}-\beta _{2}q^{5}-q^{7}-\beta _{2}q^{8}+\cdots\)
3330.2.h.k 3330.h 37.b $4$ $26.590$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+\beta _{2}q^{5}+(1-\beta _{3})q^{7}+\cdots\)
3330.2.h.l 3330.h 37.b $4$ $26.590$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{4}+\zeta_{12}q^{5}+q^{7}-\zeta_{12}q^{8}+\cdots\)
3330.2.h.m 3330.h 37.b $6$ $26.590$ 6.0.279290944.1 None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+\beta _{2}q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\)
3330.2.h.n 3330.h 37.b $6$ $26.590$ 6.0.399424.1 None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+\beta _{2}q^{5}+(2+\beta _{3})q^{7}+\cdots\)
3330.2.h.o 3330.h 37.b $8$ $26.590$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}-\beta _{2}q^{5}-\beta _{5}q^{7}-\beta _{2}q^{8}+\cdots\)
3330.2.h.p 3330.h 37.b $16$ $26.590$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}-q^{4}+\beta _{10}q^{5}+\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)