Properties

Label 2550.2.d
Level $2550$
Weight $2$
Character orbit 2550.d
Rep. character $\chi_{2550}(2449,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $22$
Sturm bound $1080$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2550.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1080\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2550, [\chi])\).

Total New Old
Modular forms 564 48 516
Cusp forms 516 48 468
Eisenstein series 48 0 48

Trace form

\( 48q - 48q^{4} + 4q^{6} - 48q^{9} + O(q^{10}) \) \( 48q - 48q^{4} + 4q^{6} - 48q^{9} - 16q^{11} + 16q^{14} + 48q^{16} + 8q^{21} - 4q^{24} - 16q^{26} - 32q^{29} + 16q^{31} - 8q^{34} + 48q^{36} - 8q^{39} + 32q^{41} + 16q^{44} - 48q^{49} + 4q^{51} - 4q^{54} - 16q^{56} - 16q^{59} - 48q^{64} - 8q^{69} + 16q^{74} - 16q^{79} + 48q^{81} - 8q^{84} + 32q^{86} + 64q^{89} + 48q^{91} + 32q^{94} + 4q^{96} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2550, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2550.2.d.a \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
2550.2.d.b \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2550.2.d.c \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
2550.2.d.d \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
2550.2.d.e \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2550.2.d.f \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2550.2.d.g \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2550.2.d.h \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2550.2.d.i \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
2550.2.d.j \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2550.2.d.k \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
2550.2.d.l \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
2550.2.d.m \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
2550.2.d.n \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2550.2.d.o \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
2550.2.d.p \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+5iq^{7}+\cdots\)
2550.2.d.q \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2550.2.d.r \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2550.2.d.s \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
2550.2.d.t \(2\) \(20.362\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
2550.2.d.u \(4\) \(20.362\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+q^{6}+\beta _{2}q^{7}+\cdots\)
2550.2.d.v \(4\) \(20.362\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(850, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)