Properties

Label 405.2.e
Level $405$
Weight $2$
Character orbit 405.e
Rep. character $\chi_{405}(136,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $12$
Sturm bound $108$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(108\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 132 32 100
Cusp forms 84 32 52
Eisenstein series 48 0 48

Trace form

\( 32q - 16q^{4} + 10q^{7} + O(q^{10}) \) \( 32q - 16q^{4} + 10q^{7} + 10q^{13} - 16q^{16} + 4q^{19} - 12q^{22} - 16q^{25} - 80q^{28} + 40q^{31} + 18q^{34} - 20q^{37} + 30q^{40} + 28q^{43} - 36q^{46} - 18q^{49} + 4q^{52} - 36q^{58} - 14q^{61} + 44q^{64} - 14q^{67} - 12q^{70} + 76q^{73} + 34q^{76} - 2q^{79} + 96q^{82} - 12q^{85} - 36q^{88} - 52q^{91} - 48q^{94} - 26q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
405.2.e.a \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(0\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
405.2.e.b \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(3\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
405.2.e.c \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}-3q^{8}+\cdots\)
405.2.e.d \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
405.2.e.e \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
405.2.e.f \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+3q^{8}+\cdots\)
405.2.e.g \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(1\) \(0\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+2q^{10}+\cdots\)
405.2.e.h \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(1\) \(3\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
405.2.e.i \(4\) \(3.234\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(2\) \(6\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
405.2.e.j \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-1\) \(0\) \(2\) \(-2\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.e.k \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(0\) \(-2\) \(-2\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.e.l \(4\) \(3.234\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-2\) \(6\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)