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Properties

Label 48.7.e
Level $48$
Weight $7$
Character orbit 48.e
Rep. character $\chi_{48}(17,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(48, [\chi])\).

Total New Old
Modular forms 54 13 41
Cusp forms 42 11 31
Eisenstein series 12 2 10

Trace form

\( 11 q + q^{3} - 358 q^{7} - 461 q^{9} + O(q^{10}) \) \( 11 q + q^{3} - 358 q^{7} - 461 q^{9} - 2 q^{13} - 32 q^{15} - 7006 q^{19} - 8754 q^{21} - 9949 q^{25} - 13031 q^{27} + 34058 q^{31} + 13088 q^{33} + 56494 q^{37} - 47174 q^{39} + 55250 q^{43} - 61376 q^{45} + 128433 q^{49} + 80000 q^{51} + 189504 q^{55} - 178586 q^{57} + 95710 q^{61} - 457782 q^{63} - 310654 q^{67} - 132160 q^{69} + 69094 q^{73} + 392009 q^{75} + 896618 q^{79} - 221477 q^{81} - 562944 q^{85} - 1841760 q^{87} - 1950236 q^{91} + 486430 q^{93} + 381910 q^{97} + 3371456 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.7.e.a 48.e 3.b $1$ $11.043$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(27\) \(0\) \(286\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{3}q^{3}+286q^{7}+3^{6}q^{9}+506q^{13}+\cdots\)
48.7.e.b 48.e 3.b $2$ $11.043$ \(\Q(\sqrt{-2}) \) None \(0\) \(-42\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-21+\beta )q^{3}+10\beta q^{5}-2q^{7}+(153+\cdots)q^{9}+\cdots\)
48.7.e.c 48.e 3.b $2$ $11.043$ \(\Q(\sqrt{-5}) \) None \(0\) \(6\) \(0\) \(-484\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta )q^{3}-6\beta q^{5}-242q^{7}+(-711+\cdots)q^{9}+\cdots\)
48.7.e.d 48.e 3.b $6$ $11.043$ 6.0.1173604352.2 None \(0\) \(10\) \(0\) \(-156\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3^{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)