Properties

Label 49.10.c
Level $49$
Weight $10$
Character orbit 49.c
Rep. character $\chi_{49}(18,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $8$
Sturm bound $46$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(46\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(49, [\chi])\).

Total New Old
Modular forms 92 64 28
Cusp forms 76 56 20
Eisenstein series 16 8 8

Trace form

\( 56 q + 35 q^{2} - 161 q^{3} - 6825 q^{4} - 1533 q^{5} + 8708 q^{6} - 68250 q^{8} - 142261 q^{9} - 4298 q^{10} - 59731 q^{11} - 135604 q^{12} + 319676 q^{13} - 181118 q^{15} - 2079973 q^{16} - 324681 q^{17}+ \cdots - 3174578428 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.10.c.a 49.c 7.c $2$ $25.237$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) 49.10.a.a \(5\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+5\zeta_{6}q^{2}+(487-487\zeta_{6})q^{4}+4995q^{8}+\cdots\)
49.10.c.b 49.c 7.c $4$ $25.237$ \(\Q(\sqrt{-3}, \sqrt{193})\) None 7.10.a.a \(6\) \(-86\) \(-2238\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3\beta _{1}+\beta _{2})q^{2}+(-43+43\beta _{1}-11\beta _{2}+\cdots)q^{3}+\cdots\)
49.10.c.c 49.c 7.c $4$ $25.237$ \(\Q(\sqrt{-3}, \sqrt{193})\) None 7.10.a.a \(6\) \(86\) \(2238\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3\beta _{1}+\beta _{2})q^{2}+(43-43\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots\)
49.10.c.d 49.c 7.c $6$ $25.237$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 7.10.a.b \(-21\) \(-84\) \(-1554\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(7\beta _{3}-\beta _{5})q^{2}+(-28+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
49.10.c.e 49.c 7.c $6$ $25.237$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 7.10.a.b \(-21\) \(84\) \(1554\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(7\beta _{3}-\beta _{5})q^{2}+(28-\beta _{1}-\beta _{2}+28\beta _{3}+\cdots)q^{3}+\cdots\)
49.10.c.f 49.c 7.c $8$ $25.237$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 49.10.a.d \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\beta _{1}-\beta _{3}+\beta _{5})q^{2}+\beta _{2}q^{3}+\cdots\)
49.10.c.g 49.c 7.c $10$ $25.237$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 7.10.c.a \(-18\) \(-161\) \(-1533\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(-33+\beta _{1}+\cdots)q^{3}+\cdots\)
49.10.c.h 49.c 7.c $16$ $25.237$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 49.10.a.g \(66\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-8\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-\beta _{4}-\beta _{8}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(49, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)