Properties

Label 3600.2.f
Level $3600$
Weight $2$
Character orbit 3600.f
Rep. character $\chi_{3600}(2449,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $22$
Sturm bound $1440$
Trace bound $29$

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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1440\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

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

Total New Old
Modular forms 792 46 746
Cusp forms 648 44 604
Eisenstein series 144 2 142

Trace form

\( 44q + O(q^{10}) \) \( 44q + 4q^{11} - 4q^{19} - 12q^{29} + 16q^{31} - 8q^{41} - 20q^{49} - 16q^{61} - 56q^{71} - 32q^{79} + 24q^{89} + O(q^{100}) \)

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.f.a \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-6q^{11}-2iq^{13}+3iq^{17}+\cdots\)
3600.2.f.b \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+5iq^{7}-6q^{11}+3iq^{13}+2iq^{17}+\cdots\)
3600.2.f.c \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4q^{11}-3iq^{13}+3iq^{17}-4q^{19}+\cdots\)
3600.2.f.d \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-4q^{11}-iq^{13}-4iq^{17}+\cdots\)
3600.2.f.e \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4q^{11}+iq^{13}-iq^{17}+4q^{19}+\cdots\)
3600.2.f.f \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-3q^{11}-4iq^{13}-3iq^{17}+\cdots\)
3600.2.f.g \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}+2iq^{13}+iq^{17}+\cdots\)
3600.2.f.h \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+7iq^{13}-7q^{19}-11q^{31}+\cdots\)
3600.2.f.i \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-iq^{13}-3iq^{17}-4q^{19}+\cdots\)
3600.2.f.j \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+iq^{13}-3iq^{17}-4q^{19}+\cdots\)
3600.2.f.k \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+iq^{13}-q^{19}+7q^{31}+2iq^{37}+\cdots\)
3600.2.f.l \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-3iq^{13}-iq^{17}+4q^{19}+\cdots\)
3600.2.f.m \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-iq^{13}+8q^{19}+4q^{31}+\cdots\)
3600.2.f.n \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+q^{11}+4iq^{13}+5iq^{17}+\cdots\)
3600.2.f.o \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+2q^{11}-3iq^{13}+6iq^{17}+\cdots\)
3600.2.f.p \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+2q^{11}-iq^{13}-2iq^{17}+\cdots\)
3600.2.f.q \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}+2iq^{13}-iq^{17}+\cdots\)
3600.2.f.r \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4q^{11}-iq^{13}+iq^{17}-4q^{19}+\cdots\)
3600.2.f.s \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+4q^{11}-iq^{13}+4iq^{17}+\cdots\)
3600.2.f.t \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+4q^{11}+iq^{13}-iq^{17}+\cdots\)
3600.2.f.u \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+6q^{11}-2iq^{13}-3iq^{17}+\cdots\)
3600.2.f.v \(2\) \(28.746\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+6q^{11}-5iq^{13}+6iq^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)