Properties

Label 5148.2.a
Level $5148$
Weight $2$
Character orbit 5148.a
Rep. character $\chi_{5148}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $20$
Sturm bound $2016$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5148.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(2016\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5148))\).

Total New Old
Modular forms 1032 50 982
Cusp forms 985 50 935
Eisenstein series 47 0 47

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

\(2\)\(3\)\(11\)\(13\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(25\)
Minus space\(-\)\(25\)

Trace form

\( 50q - 2q^{5} + O(q^{10}) \) \( 50q - 2q^{5} - 2q^{11} + 8q^{17} - 4q^{19} - 6q^{23} + 40q^{25} - 24q^{29} - 14q^{31} + 4q^{35} - 14q^{37} - 12q^{41} + 8q^{43} - 16q^{47} + 54q^{49} + 8q^{53} - 6q^{55} - 2q^{59} + 20q^{61} - 4q^{65} + 10q^{67} + 50q^{71} + 28q^{73} - 4q^{77} + 28q^{79} + 32q^{83} - 4q^{85} - 42q^{89} + 4q^{91} - 68q^{95} - 30q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5148))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11 13
5148.2.a.a \(1\) \(41.107\) \(\Q\) None \(0\) \(0\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q-3q^{5}+2q^{7}-q^{11}+q^{13}+2q^{19}+\cdots\)
5148.2.a.b \(1\) \(41.107\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q-2q^{5}+q^{11}+q^{13}+6q^{17}+4q^{23}+\cdots\)
5148.2.a.c \(1\) \(41.107\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(-\) \(q-2q^{7}+q^{11}+q^{13}+2q^{17}+6q^{19}+\cdots\)
5148.2.a.d \(1\) \(41.107\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+2q^{7}+q^{11}+q^{13}-6q^{17}+2q^{19}+\cdots\)
5148.2.a.e \(1\) \(41.107\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+2q^{5}-2q^{7}-q^{11}+q^{13}+2q^{19}+\cdots\)
5148.2.a.f \(1\) \(41.107\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{5}-q^{11}+q^{13}-6q^{17}-4q^{23}+\cdots\)
5148.2.a.g \(2\) \(41.107\) \(\Q(\sqrt{21}) \) None \(0\) \(0\) \(-4\) \(5\) \(-\) \(-\) \(-\) \(+\) \(q-2q^{5}+(2+\beta )q^{7}+q^{11}-q^{13}+4q^{17}+\cdots\)
5148.2.a.h \(2\) \(41.107\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+(-1-\beta )q^{7}+q^{11}+q^{13}+2\beta q^{17}+\cdots\)
5148.2.a.i \(2\) \(41.107\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{5}-q^{11}-q^{13}+(1-3\beta )q^{17}+\cdots\)
5148.2.a.j \(2\) \(41.107\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+(2+\beta )q^{5}+2\beta q^{7}+q^{11}-q^{13}+\cdots\)
5148.2.a.k \(2\) \(41.107\) \(\Q(\sqrt{21}) \) None \(0\) \(0\) \(4\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+2q^{5}+(2-\beta )q^{7}-q^{11}+q^{13}+(-3+\cdots)q^{19}+\cdots\)
5148.2.a.l \(3\) \(41.107\) 3.3.404.1 None \(0\) \(0\) \(-4\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+(-1-2\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
5148.2.a.m \(3\) \(41.107\) 3.3.564.1 None \(0\) \(0\) \(-2\) \(4\) \(-\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}-q^{11}+\cdots\)
5148.2.a.n \(3\) \(41.107\) 3.3.1620.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
5148.2.a.o \(3\) \(41.107\) 3.3.229.1 None \(0\) \(0\) \(1\) \(-7\) \(-\) \(-\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{5}+(-2-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
5148.2.a.p \(4\) \(41.107\) 4.4.82128.1 None \(0\) \(0\) \(-4\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
5148.2.a.q \(4\) \(41.107\) 4.4.90996.1 None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{5}+(1+\beta _{2})q^{7}-q^{11}+q^{13}+\cdots\)
5148.2.a.r \(4\) \(41.107\) 4.4.82128.1 None \(0\) \(0\) \(4\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots\)
5148.2.a.s \(5\) \(41.107\) 5.5.815952.1 None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-\beta _{4}q^{5}+\beta _{3}q^{7}+q^{11}-q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
5148.2.a.t \(5\) \(41.107\) 5.5.815952.1 None \(0\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+\beta _{4}q^{5}+\beta _{3}q^{7}-q^{11}-q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2574))\)\(^{\oplus 2}\)