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Properties

Label 1014.4.b
Level $1014$
Weight $4$
Character orbit 1014.b
Rep. character $\chi_{1014}(337,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $17$
Sturm bound $728$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1014.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(728\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1014, [\chi])\).

Total New Old
Modular forms 574 78 496
Cusp forms 518 78 440
Eisenstein series 56 0 56

Trace form

\( 78 q - 6 q^{3} - 312 q^{4} + 702 q^{9} + O(q^{10}) \) \( 78 q - 6 q^{3} - 312 q^{4} + 702 q^{9} - 104 q^{10} + 24 q^{12} - 96 q^{14} + 1248 q^{16} + 192 q^{17} + 200 q^{22} - 8 q^{23} - 1658 q^{25} - 54 q^{27} - 56 q^{29} - 120 q^{30} + 1560 q^{35} - 2808 q^{36} - 704 q^{38} + 416 q^{40} + 168 q^{42} - 1064 q^{43} - 96 q^{48} - 3330 q^{49} + 348 q^{51} - 528 q^{53} - 336 q^{55} + 384 q^{56} - 2352 q^{61} - 2464 q^{62} - 4992 q^{64} + 1152 q^{66} - 768 q^{68} - 1992 q^{69} + 704 q^{74} + 1674 q^{75} + 1256 q^{77} + 3300 q^{79} + 6318 q^{81} + 224 q^{82} - 2736 q^{87} - 800 q^{88} - 936 q^{90} + 32 q^{92} + 1088 q^{94} - 224 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1014.4.b.a 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.a.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3q^{3}-4q^{4}+8iq^{5}-3iq^{6}+\cdots\)
1014.4.b.b 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.e.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-3q^{3}-4q^{4}+7iq^{5}-6iq^{6}+\cdots\)
1014.4.b.c 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.a.e \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3q^{3}-4q^{4}+3iq^{5}-3iq^{6}+\cdots\)
1014.4.b.d 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 6.4.a.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-3q^{3}-4q^{4}+3iq^{5}+3iq^{6}+\cdots\)
1014.4.b.e 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.a.d \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-3q^{3}-4q^{4}+10iq^{5}+3iq^{6}+\cdots\)
1014.4.b.f 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.a.b \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3q^{3}-4q^{4}+8iq^{5}+3iq^{6}+\cdots\)
1014.4.b.g 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.a.f \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3q^{3}-4q^{4}+2iq^{5}+3iq^{6}+\cdots\)
1014.4.b.h 1014.b 13.b $2$ $59.828$ \(\Q(\sqrt{-1}) \) None 78.4.a.c \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+3q^{3}-4q^{4}+5iq^{5}-3iq^{6}+\cdots\)
1014.4.b.i 1014.b 13.b $4$ $59.828$ \(\Q(i, \sqrt{61})\) None 78.4.e.c \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-3q^{3}-4q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.j 1014.b 13.b $4$ $59.828$ \(\Q(i, \sqrt{673})\) None 78.4.e.b \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}-6\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.k 1014.b 13.b $4$ $59.828$ \(\Q(\zeta_{12})\) None 78.4.i.a \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{12}q^{2}+3q^{3}-4q^{4}+(6\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1014.4.b.l 1014.b 13.b $6$ $59.828$ 6.0.153664.1 None 1014.4.a.t \(0\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{5}q^{2}-3q^{3}-4q^{4}+(-2\beta _{1}-3\beta _{3}+\cdots)q^{5}+\cdots\)
1014.4.b.m 1014.b 13.b $6$ $59.828$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 78.4.e.d \(0\) \(18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{2}q^{2}+3q^{3}-4q^{4}+(\beta _{1}+4\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.n 1014.b 13.b $6$ $59.828$ 6.0.153664.1 None 1014.4.a.v \(0\) \(18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{5}q^{2}+3q^{3}-4q^{4}+(3\beta _{1}+5\beta _{3}+\cdots)q^{5}+\cdots\)
1014.4.b.o 1014.b 13.b $8$ $59.828$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 78.4.i.b \(0\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-3q^{3}-4q^{4}+(3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1014.4.b.p 1014.b 13.b $12$ $59.828$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1014.4.a.bb \(0\) \(-36\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{7}q^{2}-3q^{3}-4q^{4}+(-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
1014.4.b.q 1014.b 13.b $12$ $59.828$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1014.4.a.bc \(0\) \(36\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{3}q^{2}+3q^{3}-4q^{4}+\beta _{8}q^{5}-6\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)