Properties

Label 3600.2.w
Level $3600$
Weight $2$
Character orbit 3600.w
Rep. character $\chi_{3600}(593,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $13$
Sturm bound $1440$
Trace bound $31$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3600.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 13 \)
Sturm bound: \(1440\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3600, [\chi])\).

Total New Old
Modular forms 1584 72 1512
Cusp forms 1296 72 1224
Eisenstein series 288 0 288

Trace form

\( 72q + O(q^{10}) \) \( 72q - 32q^{31} - 8q^{37} - 32q^{43} - 64q^{61} - 48q^{67} + 16q^{73} - 48q^{91} + 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3600.2.w.a \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-12\) \(q+(-3+3\zeta_{8})q^{7}-\zeta_{8}^{2}q^{11}+(3+3\zeta_{8}+\cdots)q^{13}+\cdots\)
3600.2.w.b \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) \(q+(-2+2\zeta_{8})q^{7}-2\zeta_{8}^{2}q^{11}+(-1+\cdots)q^{13}+\cdots\)
3600.2.w.c \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q+(-1+\zeta_{8})q^{7}+\zeta_{8}^{2}q^{11}+(-3-3\zeta_{8}+\cdots)q^{13}+\cdots\)
3600.2.w.d \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-4\zeta_{8}^{2}q^{11}+(-3+3\zeta_{8})q^{13}+4\zeta_{8}q^{19}+\cdots\)
3600.2.w.e \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q+(1-\zeta_{8})q^{7}+\zeta_{8}^{2}q^{11}+(3+3\zeta_{8}+\cdots)q^{13}+\cdots\)
3600.2.w.f \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) \(q+(2-2\zeta_{8})q^{7}+2\zeta_{8}^{2}q^{11}+(-3-3\zeta_{8}+\cdots)q^{13}+\cdots\)
3600.2.w.g \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) \(q+(2-2\zeta_{8})q^{7}+2\zeta_{8}^{2}q^{11}+(3+3\zeta_{8}+\cdots)q^{13}+\cdots\)
3600.2.w.h \(4\) \(28.746\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(12\) \(q+(3-3\zeta_{8})q^{7}+\zeta_{8}^{2}q^{11}+(-3-3\zeta_{8}+\cdots)q^{13}+\cdots\)
3600.2.w.i \(8\) \(28.746\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-16\) \(q+(-2+2\zeta_{24}^{2}-\zeta_{24}^{3})q^{7}+\zeta_{24}^{6}q^{11}+\cdots\)
3600.2.w.j \(8\) \(28.746\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(-8\) \(q+(-1+\beta _{1}+\beta _{4})q^{7}+(-\beta _{3}-\beta _{6}+\cdots)q^{11}+\cdots\)
3600.2.w.k \(8\) \(28.746\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{7}+\zeta_{24}^{5}q^{11}+\zeta_{24}q^{13}+\cdots\)
3600.2.w.l \(8\) \(28.746\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{7}+\zeta_{24}^{7}q^{11}+3\zeta_{24}q^{13}+\cdots\)
3600.2.w.m \(8\) \(28.746\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(16\) \(q+(2-\zeta_{24}+2\zeta_{24}^{2})q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)