Properties

Label 4950.2.c
Level $4950$
Weight $2$
Character orbit 4950.c
Rep. character $\chi_{4950}(199,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $31$
Sturm bound $2160$
Trace bound $26$

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Defining parameters

Level: \( N \) \(=\) \( 4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4950.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 31 \)
Sturm bound: \(2160\)
Trace bound: \(26\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4950, [\chi])\).

Total New Old
Modular forms 1128 74 1054
Cusp forms 1032 74 958
Eisenstein series 96 0 96

Trace form

\( 74 q - 74 q^{4} + O(q^{10}) \) \( 74 q - 74 q^{4} + 2 q^{11} + 74 q^{16} - 8 q^{19} + 20 q^{29} + 12 q^{31} + 20 q^{34} - 36 q^{41} - 2 q^{44} + 24 q^{46} - 114 q^{49} + 36 q^{61} - 74 q^{64} + 92 q^{71} + 12 q^{74} + 8 q^{76} - 56 q^{79} + 28 q^{86} - 48 q^{89} + 104 q^{91} - 56 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4950, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4950.2.c.a 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+5iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.b 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.c 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.d 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.e 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.f 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-q^{11}+\cdots\)
4950.2.c.g 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}-q^{11}-2iq^{13}+\cdots\)
4950.2.c.h 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{8}-q^{11}+q^{16}+\cdots\)
4950.2.c.i 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}-q^{11}+3iq^{13}+\cdots\)
4950.2.c.j 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{8}-q^{11}-6iq^{13}+\cdots\)
4950.2.c.k 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.l 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.m 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.n 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+3iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.o 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}-q^{11}+\cdots\)
4950.2.c.p 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.q 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.r 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.s 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.t 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+q^{11}+\cdots\)
4950.2.c.u 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{8}+q^{11}+q^{16}+\cdots\)
4950.2.c.v 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-iq^{8}+q^{11}-2iq^{13}+\cdots\)
4950.2.c.w 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.x 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+2iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.y 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.z 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.ba 4950.c 5.b $2$ $39.526$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+4iq^{7}+iq^{8}+q^{11}+\cdots\)
4950.2.c.bb 4950.c 5.b $4$ $39.526$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+q^{11}+\cdots\)
4950.2.c.bc 4950.c 5.b $4$ $39.526$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+q^{11}+\cdots\)
4950.2.c.bd 4950.c 5.b $6$ $39.526$ 6.0.270273600.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+\beta _{3}q^{7}-\beta _{1}q^{8}-q^{11}+\cdots\)
4950.2.c.be 4950.c 5.b $6$ $39.526$ 6.0.270273600.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+\beta _{3}q^{7}+\beta _{1}q^{8}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(990, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2475, [\chi])\)\(^{\oplus 2}\)