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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2550.2.d.a 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
2550.2.d.b 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2550.2.d.c 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
2550.2.d.d 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
2550.2.d.e 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.p \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2550.2.d.f 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2550.2.d.g 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 102.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2550.2.d.h 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.q \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2550.2.d.i 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
2550.2.d.j 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2550.2.d.k 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
2550.2.d.l 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
2550.2.d.m 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 102.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
2550.2.d.n 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2550.2.d.o 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
2550.2.d.p 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+5iq^{7}+\cdots\)
2550.2.d.q 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 102.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2550.2.d.r 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2550.2.d.s 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 510.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
2550.2.d.t 2550.d 5.b $2$ $20.362$ \(\Q(\sqrt{-1}) \) None 2550.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
2550.2.d.u 2550.d 5.b $4$ $20.362$ \(\Q(i, \sqrt{6})\) None 510.2.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+q^{6}+\beta _{2}q^{7}+\cdots\)
2550.2.d.v 2550.d 5.b $4$ $20.362$ \(\Q(i, \sqrt{33})\) None 2550.2.a.bg \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)

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

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