Properties

Label 2400.2.f
Level $2400$
Weight $2$
Character orbit 2400.f
Rep. character $\chi_{2400}(1249,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $18$
Sturm bound $960$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2400.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(960\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).

Total New Old
Modular forms 528 36 492
Cusp forms 432 36 396
Eisenstein series 96 0 96

Trace form

\( 36q - 36q^{9} + O(q^{10}) \) \( 36q - 36q^{9} - 8q^{29} - 56q^{41} - 20q^{49} + 8q^{61} + 36q^{81} + 56q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2400.2.f.a \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+4iq^{7}-q^{9}-4q^{11}+2iq^{13}+\cdots\)
2400.2.f.b \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}-q^{9}-4q^{11}+7iq^{13}+\cdots\)
2400.2.f.c \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots\)
2400.2.f.d \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+4iq^{7}-q^{9}-4q^{11}-6iq^{13}+\cdots\)
2400.2.f.e \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}-4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
2400.2.f.f \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}-q^{9}-5iq^{13}-5q^{19}+\cdots\)
2400.2.f.g \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+2iq^{13}-6iq^{17}-4q^{19}+\cdots\)
2400.2.f.h \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{7}-q^{9}-iq^{13}-3q^{19}+\cdots\)
2400.2.f.i \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+4iq^{7}-q^{9}-2iq^{13}+6iq^{17}+\cdots\)
2400.2.f.j \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+4iq^{7}-q^{9}+2iq^{13}-6iq^{17}+\cdots\)
2400.2.f.k \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{7}-q^{9}+iq^{13}+3q^{19}+\cdots\)
2400.2.f.l \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}-2iq^{13}+6iq^{17}+4q^{19}+\cdots\)
2400.2.f.m \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}-q^{9}+5iq^{13}+5q^{19}+\cdots\)
2400.2.f.n \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
2400.2.f.o \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+4iq^{7}-q^{9}+4q^{11}+6iq^{13}+\cdots\)
2400.2.f.p \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots\)
2400.2.f.q \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}-q^{9}+4q^{11}-7iq^{13}+\cdots\)
2400.2.f.r \(2\) \(19.164\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+4iq^{7}-q^{9}+4q^{11}-2iq^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)