Properties

Label 3330.2.d
Level $3330$
Weight $2$
Character orbit 3330.d
Rep. character $\chi_{3330}(1999,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $18$
Sturm bound $1368$
Trace bound $14$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(1368\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(29\)

Dimensions

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

Total New Old
Modular forms 700 90 610
Cusp forms 668 90 578
Eisenstein series 32 0 32

Trace form

\( 90 q - 90 q^{4} - 4 q^{5} + O(q^{10}) \) \( 90 q - 90 q^{4} - 4 q^{5} + 4 q^{10} + 16 q^{11} + 4 q^{14} + 90 q^{16} + 12 q^{19} + 4 q^{20} - 8 q^{25} - 16 q^{29} - 8 q^{31} - 4 q^{40} + 4 q^{41} - 16 q^{44} - 12 q^{46} - 78 q^{49} - 8 q^{50} + 20 q^{55} - 4 q^{56} - 4 q^{59} - 90 q^{64} - 24 q^{65} - 8 q^{71} + 10 q^{74} - 12 q^{76} + 32 q^{79} - 4 q^{80} - 12 q^{85} + 52 q^{86} + 60 q^{89} - 112 q^{91} + 28 q^{94} - 4 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3330.2.d.a 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 1110.2.d.e \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots\)
3330.2.d.b 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 1110.2.d.d \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots\)
3330.2.d.c 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 370.2.b.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
3330.2.d.d 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 1110.2.d.c \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots\)
3330.2.d.e 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 1110.2.d.b \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(1-2i)q^{5}+5iq^{7}+\cdots\)
3330.2.d.f 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 370.2.b.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2-i)q^{5}+2iq^{7}-iq^{8}+\cdots\)
3330.2.d.g 3330.d 5.b $2$ $26.590$ \(\Q(\sqrt{-1}) \) None 1110.2.d.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(2+i)q^{5}+2iq^{7}+iq^{8}+\cdots\)
3330.2.d.h 3330.d 5.b $4$ $26.590$ \(\Q(i, \sqrt{6})\) None 1110.2.d.h \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
3330.2.d.i 3330.d 5.b $4$ $26.590$ \(\Q(\zeta_{12})\) None 3330.2.d.i \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{4}+(-1-2\zeta_{12})q^{5}+\cdots\)
3330.2.d.j 3330.d 5.b $4$ $26.590$ \(\Q(i, \sqrt{5})\) None 1110.2.d.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{7}-\beta _{1}q^{8}+\cdots\)
3330.2.d.k 3330.d 5.b $4$ $26.590$ \(\Q(\zeta_{8})\) None 1110.2.d.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
3330.2.d.l 3330.d 5.b $4$ $26.590$ \(\Q(\zeta_{12})\) None 3330.2.d.i \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}-q^{4}+(1+2\zeta_{12})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
3330.2.d.m 3330.d 5.b $4$ $26.590$ \(\Q(i, \sqrt{6})\) None 370.2.b.c \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+(2-\beta _{1})q^{5}+(2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
3330.2.d.n 3330.d 5.b $6$ $26.590$ 6.0.5161984.1 None 1110.2.d.i \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3330.2.d.o 3330.d 5.b $8$ $26.590$ 8.0.\(\cdots\).2 None 1110.2.d.j \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
3330.2.d.p 3330.d 5.b $10$ $26.590$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 370.2.b.d \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+(-1+\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
3330.2.d.q 3330.d 5.b $14$ $26.590$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 3330.2.d.q \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}-q^{4}+\beta _{9}q^{5}+(\beta _{6}-\beta _{7})q^{7}+\cdots\)
3330.2.d.r 3330.d 5.b $14$ $26.590$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 3330.2.d.q \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-q^{4}-\beta _{9}q^{5}+(\beta _{6}-\beta _{7})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)