Properties

Label 112.4.a
Level $112$
Weight $4$
Character orbit 112.a
Rep. character $\chi_{112}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $8$
Sturm bound $64$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 112.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(64\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(112))\).

Total New Old
Modular forms 54 9 45
Cusp forms 42 9 33
Eisenstein series 12 0 12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(4\)

Trace form

\( 9q + 2q^{5} + 7q^{7} + 101q^{9} + O(q^{10}) \) \( 9q + 2q^{5} + 7q^{7} + 101q^{9} - 76q^{11} - 46q^{13} + 72q^{15} - 102q^{17} + 24q^{19} + 56q^{23} + 247q^{25} + 576q^{27} - 242q^{29} - 264q^{31} - 384q^{33} - 210q^{35} + 326q^{37} - 264q^{39} + 98q^{41} - 28q^{43} + 90q^{45} + 792q^{47} + 441q^{49} - 1200q^{51} - 98q^{53} - 1080q^{55} + 40q^{57} - 960q^{59} - 1302q^{61} + 315q^{63} - 116q^{65} + 36q^{67} - 528q^{69} + 840q^{71} + 458q^{73} + 2720q^{75} + 476q^{77} + 304q^{79} + 1577q^{81} + 1112q^{83} - 700q^{85} - 16q^{87} - 150q^{89} - 546q^{91} - 1680q^{93} + 1192q^{95} + 906q^{97} + 2308q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(112))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
112.4.a.a \(1\) \(6.608\) \(\Q\) None \(0\) \(-8\) \(-14\) \(7\) \(-\) \(-\) \(q-8q^{3}-14q^{5}+7q^{7}+37q^{9}+28q^{11}+\cdots\)
112.4.a.b \(1\) \(6.608\) \(\Q\) None \(0\) \(-6\) \(8\) \(7\) \(+\) \(-\) \(q-6q^{3}+8q^{5}+7q^{7}+9q^{9}-56q^{11}+\cdots\)
112.4.a.c \(1\) \(6.608\) \(\Q\) None \(0\) \(-4\) \(6\) \(-7\) \(-\) \(+\) \(q-4q^{3}+6q^{5}-7q^{7}-11q^{9}+12q^{11}+\cdots\)
112.4.a.d \(1\) \(6.608\) \(\Q\) None \(0\) \(2\) \(-16\) \(7\) \(+\) \(-\) \(q+2q^{3}-2^{4}q^{5}+7q^{7}-23q^{9}-24q^{11}+\cdots\)
112.4.a.e \(1\) \(6.608\) \(\Q\) None \(0\) \(2\) \(-12\) \(-7\) \(-\) \(+\) \(q+2q^{3}-12q^{5}-7q^{7}-23q^{9}-48q^{11}+\cdots\)
112.4.a.f \(1\) \(6.608\) \(\Q\) None \(0\) \(2\) \(16\) \(7\) \(-\) \(-\) \(q+2q^{3}+2^{4}q^{5}+7q^{7}-23q^{9}+8q^{11}+\cdots\)
112.4.a.g \(1\) \(6.608\) \(\Q\) None \(0\) \(10\) \(-8\) \(7\) \(-\) \(-\) \(q+10q^{3}-8q^{5}+7q^{7}+73q^{9}+40q^{11}+\cdots\)
112.4.a.h \(2\) \(6.608\) \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(22\) \(-14\) \(+\) \(+\) \(q+(1+\beta )q^{3}+(11+\beta )q^{5}-7q^{7}+(31+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(112))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(112)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)