Properties

Label 1521.2.b
Level $1521$
Weight $2$
Character orbit 1521.b
Rep. character $\chi_{1521}(1351,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $14$
Sturm bound $364$
Trace bound $43$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(364\)
Trace bound: \(43\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1521, [\chi])\).

Total New Old
Modular forms 210 68 142
Cusp forms 154 58 96
Eisenstein series 56 10 46

Trace form

\( 58 q - 48 q^{4} + O(q^{10}) \) \( 58 q - 48 q^{4} + 8 q^{10} + 26 q^{14} + 16 q^{16} - 14 q^{17} + 14 q^{22} - 2 q^{23} - 32 q^{25} + 16 q^{29} - 4 q^{35} - 4 q^{38} - 76 q^{40} + 30 q^{43} - 44 q^{49} + 32 q^{53} - 44 q^{55} - 8 q^{56} + 6 q^{61} + 10 q^{62} + 54 q^{64} + 72 q^{68} - 26 q^{74} - 24 q^{77} - 2 q^{79} - 66 q^{82} - 70 q^{88} + 16 q^{92} - 2 q^{94} - 2 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1521.2.b.a 1521.b 13.b $2$ $12.145$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{8}+3q^{10}+\cdots\)
1521.2.b.b 1521.b 13.b $2$ $12.145$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+2iq^{5}-4iq^{7}+3iq^{8}+\cdots\)
1521.2.b.c 1521.b 13.b $2$ $12.145$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-iq^{5}+2iq^{7}+3iq^{8}+\cdots\)
1521.2.b.d 1521.b 13.b $2$ $12.145$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+3\zeta_{6}q^{7}+4q^{16}-2\zeta_{6}q^{19}+\cdots\)
1521.2.b.e 1521.b 13.b $2$ $12.145$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+iq^{7}+4q^{16}+8iq^{19}+5q^{25}+\cdots\)
1521.2.b.f 1521.b 13.b $2$ $12.145$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+2\zeta_{6}q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{11}+\cdots\)
1521.2.b.g 1521.b 13.b $4$ $12.145$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{5}-2\beta _{2}q^{7}+\cdots\)
1521.2.b.h 1521.b 13.b $4$ $12.145$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1521.2.b.i 1521.b 13.b $4$ $12.145$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}-q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
1521.2.b.j 1521.b 13.b $4$ $12.145$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1521.2.b.k 1521.b 13.b $6$ $12.145$ 6.0.153664.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-3-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
1521.2.b.l 1521.b 13.b $6$ $12.145$ 6.0.153664.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{5})q^{2}+(1-2\beta _{2}-\beta _{4})q^{4}+\cdots\)
1521.2.b.m 1521.b 13.b $6$ $12.145$ 6.0.153664.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
1521.2.b.n 1521.b 13.b $12$ $12.145$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}+(-2-\beta _{2}+2\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)