↑

Properties

Label 735.2.j
Level $735$
Weight $2$
Character orbit 735.j
Rep. character $\chi_{735}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
Newform subspaces $8$
Sturm bound $224$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

Total New Old
Modular forms 256 184 72
Cusp forms 192 144 48
Eisenstein series 64 40 24

Trace form

\( 144q + 4q^{3} + O(q^{10}) \) \( 144q + 4q^{3} + 16q^{10} - 16q^{12} + 8q^{13} + 4q^{15} - 80q^{16} + 4q^{18} - 40q^{22} + 24q^{25} + 16q^{27} - 28q^{33} - 56q^{36} + 24q^{37} - 64q^{40} + 16q^{43} - 20q^{45} + 64q^{46} - 16q^{48} + 32q^{51} - 40q^{55} + 8q^{57} - 16q^{58} - 76q^{60} - 32q^{61} + 16q^{66} - 24q^{67} + 52q^{72} - 32q^{73} + 60q^{75} - 32q^{76} - 152q^{78} - 56q^{81} + 80q^{82} - 56q^{85} - 4q^{87} - 192q^{88} + 24q^{90} + 24q^{93} + 96q^{96} - 24q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
735.2.j.a \(8\) \(5.869\) \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(8\) \(0\) \(q+(2\zeta_{24}-2\zeta_{24}^{5})q^{2}+(\zeta_{24}+\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
735.2.j.b \(8\) \(5.869\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(-8\) \(0\) \(q+2\zeta_{24}^{3}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
735.2.j.c \(16\) \(5.869\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{1}-\beta _{2}-\beta _{8})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.j.d \(16\) \(5.869\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.j.e \(24\) \(5.869\) None \(0\) \(-2\) \(0\) \(0\)
735.2.j.f \(24\) \(5.869\) None \(0\) \(0\) \(0\) \(0\)
735.2.j.g \(24\) \(5.869\) None \(0\) \(2\) \(0\) \(0\)
735.2.j.h \(24\) \(5.869\) None \(0\) \(4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)