Properties

Label 2548.2.j
Level $2548$
Weight $2$
Character orbit 2548.j
Rep. character $\chi_{2548}(1145,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $19$
Sturm bound $784$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2548.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(784\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2548, [\chi])\).

Total New Old
Modular forms 832 80 752
Cusp forms 736 80 656
Eisenstein series 96 0 96

Trace form

\( 80 q - 6 q^{5} - 36 q^{9} + O(q^{10}) \) \( 80 q - 6 q^{5} - 36 q^{9} - 2 q^{11} + 4 q^{13} + 4 q^{15} - 4 q^{19} + 2 q^{23} - 50 q^{25} - 24 q^{27} - 12 q^{29} + 8 q^{33} - 8 q^{37} + 20 q^{41} - 4 q^{43} - 8 q^{45} - 6 q^{47} + 12 q^{51} + 18 q^{53} - 56 q^{55} - 10 q^{59} + 20 q^{61} + 4 q^{65} - 4 q^{67} - 40 q^{69} + 20 q^{71} - 26 q^{73} - 8 q^{75} - 6 q^{79} - 16 q^{81} + 60 q^{83} + 84 q^{85} + 16 q^{87} - 4 q^{89} + 50 q^{93} + 14 q^{95} + 4 q^{97} - 112 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2548, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2548.2.j.a 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.j.d \(0\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}-3\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
2548.2.j.b 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.j.c \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}+(3-3\zeta_{6})q^{11}+\cdots\)
2548.2.j.c 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.a.a \(0\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2548.2.j.d 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.a.b \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.e 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 52.2.a.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.f 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 52.2.a.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.g 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.a.b \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots\)
2548.2.j.h 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.j.b \(0\) \(1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
2548.2.j.i 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.j.a \(0\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
2548.2.j.j 2548.j 7.c $2$ $20.346$ \(\Q(\sqrt{-3}) \) None 364.2.a.a \(0\) \(2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2548.2.j.k 2548.j 7.c $4$ $20.346$ \(\Q(\zeta_{12})\) None 364.2.a.d \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta_{2}-\beta_1)q^{3}+(-\beta_{3}+\beta_{2})q^{5}+\cdots\)
2548.2.j.l 2548.j 7.c $4$ $20.346$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 364.2.a.c \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2548.2.j.m 2548.j 7.c $4$ $20.346$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 364.2.a.c \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-3+\cdots)q^{9}+\cdots\)
2548.2.j.n 2548.j 7.c $4$ $20.346$ \(\Q(\zeta_{12})\) None 364.2.a.d \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta_{2}+\beta_1)q^{3}+(\beta_{3}-\beta_{2})q^{5}+\cdots\)
2548.2.j.o 2548.j 7.c $6$ $20.346$ 6.0.1714608.1 None 2548.2.a.n \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{5})q^{3}+(-\beta _{1}+\beta _{4}+\beta _{5})q^{5}+\cdots\)
2548.2.j.p 2548.j 7.c $6$ $20.346$ 6.0.1714608.1 None 2548.2.a.n \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{1}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
2548.2.j.q 2548.j 7.c $8$ $20.346$ 8.0.856615824.2 None 364.2.j.e \(0\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{4})q^{3}-\beta _{6}q^{5}+(-3+3\beta _{1}+\cdots)q^{9}+\cdots\)
2548.2.j.r 2548.j 7.c $12$ $20.346$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 2548.2.a.r \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2}+\beta _{7})q^{3}+(-2+2\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots\)
2548.2.j.s 2548.j 7.c $12$ $20.346$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 2548.2.a.r \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{7})q^{3}+(2-2\beta _{6}+\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2548, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2548, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)