Properties

Label 405.2.j
Level $405$
Weight $2$
Character orbit 405.j
Rep. character $\chi_{405}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $8$
Sturm bound $108$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(108\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(405, [\chi])\).

Total New Old
Modular forms 132 52 80
Cusp forms 84 44 40
Eisenstein series 48 8 40

Trace form

\( 44 q + 24 q^{4} + O(q^{10}) \) \( 44 q + 24 q^{4} + 4 q^{10} - 20 q^{16} - 8 q^{19} + 8 q^{25} - 8 q^{31} + 26 q^{34} - 4 q^{40} + 44 q^{46} + 2 q^{49} - 96 q^{55} + 16 q^{61} - 100 q^{64} + 24 q^{70} - 18 q^{76} - 68 q^{79} - 14 q^{85} + 24 q^{91} - 136 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.2.j.a 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 405.2.b.a \(-3\) \(0\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
405.2.j.b 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 405.2.b.a \(-3\) \(0\) \(-3\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
405.2.j.c 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) 45.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots\)
405.2.j.d 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 405.2.b.a \(3\) \(0\) \(3\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.j.e 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 405.2.b.a \(3\) \(0\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.j.f 405.j 45.j $8$ $3.234$ \(\Q(\zeta_{24})\) None 135.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{4}q^{5}-\zeta_{24}q^{7}+(2\zeta_{24}^{5}+\cdots)q^{8}+\cdots\)
405.2.j.g 405.j 45.j $8$ $3.234$ \(\Q(\zeta_{24})\) None 405.2.b.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{5}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
405.2.j.h 405.j 45.j $8$ $3.234$ 8.0.12960000.1 \(\Q(\sqrt{-15}) \) 135.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\beta _{1}q^{2}+(2-\beta _{3}+2\beta _{5}+\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(405, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)