Properties

Label 624.2.cn
Level $624$
Weight $2$
Character orbit 624.cn
Rep. character $\chi_{624}(305,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $104$
Newform subspaces $6$
Sturm bound $224$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 6 \)
Sturm bound: \(224\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).

Total New Old
Modular forms 496 120 376
Cusp forms 400 104 296
Eisenstein series 96 16 80

Trace form

\( 104q + 2q^{3} + 4q^{7} - 2q^{9} + O(q^{10}) \) \( 104q + 2q^{3} + 4q^{7} - 2q^{9} - 8q^{13} + 10q^{15} + 4q^{19} + 2q^{21} + 8q^{27} + 36q^{31} - 10q^{33} + 8q^{37} - 26q^{39} + 96q^{43} - 14q^{45} + 12q^{49} + 44q^{55} - 14q^{57} - 20q^{61} - 10q^{63} + 40q^{67} - 6q^{69} - 16q^{73} - 12q^{75} + 16q^{79} - 2q^{81} - 4q^{85} + 2q^{87} - 44q^{91} - 54q^{93} - 66q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
624.2.cn.a \(4\) \(4.983\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-2\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}+\cdots)q^{7}+\cdots\)
624.2.cn.b \(4\) \(4.983\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(10\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
624.2.cn.c \(8\) \(4.983\) 8.0.56070144.2 None \(0\) \(2\) \(0\) \(4\) \(q+(\beta _{1}+\beta _{2}+\beta _{4}-2\beta _{5}-\beta _{6})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
624.2.cn.d \(16\) \(4.983\) 16.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(-8\) \(q+(-\beta _{10}-\beta _{12})q^{3}+(\beta _{1}-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots\)
624.2.cn.e \(16\) \(4.983\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q+(\beta _{9}+\beta _{13}+\beta _{15})q^{3}+(-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots\)
624.2.cn.f \(56\) \(4.983\) None \(0\) \(0\) \(0\) \(-4\)

Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)