Properties

Label 4900.2.a
Level $4900$
Weight $2$
Character orbit 4900.a
Rep. character $\chi_{4900}(1,\cdot)$
Character field $\Q$
Dimension $65$
Newform subspaces $36$
Sturm bound $1680$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(1680\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4900))\).

Total New Old
Modular forms 912 65 847
Cusp forms 769 65 704
Eisenstein series 143 0 143

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

\(2\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(19\)
Plus space\(+\)\(30\)
Minus space\(-\)\(35\)

Trace form

\( 65q + 2q^{3} + 67q^{9} + O(q^{10}) \) \( 65q + 2q^{3} + 67q^{9} - 2q^{11} - 2q^{13} - 10q^{17} + 12q^{19} + 8q^{23} + 8q^{27} - 6q^{29} - 12q^{33} - 16q^{37} - 16q^{39} + 18q^{41} - 18q^{43} - 10q^{47} + 26q^{51} - 20q^{53} + 26q^{57} + 40q^{59} + 22q^{61} - 24q^{69} - 16q^{71} + 18q^{73} - 10q^{79} + 37q^{81} - 10q^{83} - 48q^{87} - 2q^{89} - 18q^{93} + 6q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4900))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7
4900.2.a.a \(1\) \(39.127\) \(\Q\) None \(0\) \(-3\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{3}+6q^{9}-2q^{11}-6q^{13}+2q^{17}+\cdots\)
4900.2.a.b \(1\) \(39.127\) \(\Q\) None \(0\) \(-3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-3q^{3}+6q^{9}+3q^{11}-q^{13}+5q^{17}+\cdots\)
4900.2.a.c \(1\) \(39.127\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{9}-q^{11}-2q^{13}+4q^{17}+\cdots\)
4900.2.a.d \(1\) \(39.127\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{3}+q^{9}-q^{11}-2q^{13}+4q^{17}+\cdots\)
4900.2.a.e \(1\) \(39.127\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{9}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
4900.2.a.f \(1\) \(39.127\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{9}+3q^{11}-4q^{13}-2q^{19}+\cdots\)
4900.2.a.g \(1\) \(39.127\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{9}-3q^{11}-2q^{13}-3q^{17}+\cdots\)
4900.2.a.h \(1\) \(39.127\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{9}-q^{11}+5q^{13}-q^{17}+\cdots\)
4900.2.a.i \(1\) \(39.127\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
4900.2.a.j \(1\) \(39.127\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-3q^{9}-5q^{11}-6q^{13}+4q^{17}+6q^{19}+\cdots\)
4900.2.a.k \(1\) \(39.127\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-3q^{9}-5q^{11}+6q^{13}-4q^{17}+6q^{19}+\cdots\)
4900.2.a.l \(1\) \(39.127\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-3q^{9}-4q^{13}-4q^{17}-4q^{19}+8q^{23}+\cdots\)
4900.2.a.m \(1\) \(39.127\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-3q^{9}+4q^{13}+4q^{17}-4q^{19}-8q^{23}+\cdots\)
4900.2.a.n \(1\) \(39.127\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{9}-3q^{11}+2q^{13}+3q^{17}+\cdots\)
4900.2.a.o \(1\) \(39.127\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{9}-q^{11}-5q^{13}+q^{17}+\cdots\)
4900.2.a.p \(1\) \(39.127\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{9}+3q^{11}-q^{13}-3q^{17}+\cdots\)
4900.2.a.q \(1\) \(39.127\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{9}+6q^{11}+2q^{13}-6q^{17}+\cdots\)
4900.2.a.r \(1\) \(39.127\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{3}+q^{9}-q^{11}+2q^{13}-4q^{17}+\cdots\)
4900.2.a.s \(1\) \(39.127\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{9}-q^{11}+2q^{13}-4q^{17}+\cdots\)
4900.2.a.t \(1\) \(39.127\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{3}+q^{9}+3q^{11}+4q^{13}-2q^{19}+\cdots\)
4900.2.a.u \(1\) \(39.127\) \(\Q\) None \(0\) \(3\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+3q^{3}+6q^{9}-5q^{11}-3q^{13}-q^{17}+\cdots\)
4900.2.a.v \(1\) \(39.127\) \(\Q\) None \(0\) \(3\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+3q^{3}+6q^{9}-2q^{11}+6q^{13}-2q^{17}+\cdots\)
4900.2.a.w \(1\) \(39.127\) \(\Q\) None \(0\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{3}+6q^{9}+3q^{11}+q^{13}-5q^{17}+\cdots\)
4900.2.a.x \(2\) \(39.127\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+(-1+\beta )q^{3}-2\beta q^{9}+(-1-2\beta )q^{11}+\cdots\)
4900.2.a.y \(2\) \(39.127\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+2\beta q^{3}+5q^{9}+4q^{11}-3\beta q^{13}+\cdots\)
4900.2.a.z \(2\) \(39.127\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}+2\beta q^{9}+(-1+2\beta )q^{11}+\cdots\)
4900.2.a.ba \(3\) \(39.127\) 3.3.257.1 None \(0\) \(-1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{2}q^{3}+(2-\beta _{1}-\beta _{2})q^{9}+(1-\beta _{2})q^{11}+\cdots\)
4900.2.a.bb \(3\) \(39.127\) 3.3.257.1 None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+\beta _{2}q^{3}+(2-\beta _{1}-\beta _{2})q^{9}+(1-\beta _{2})q^{11}+\cdots\)
4900.2.a.bc \(3\) \(39.127\) 3.3.257.1 None \(0\) \(1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{2}q^{3}+(2-\beta _{1}-\beta _{2})q^{9}+(1-\beta _{2})q^{11}+\cdots\)
4900.2.a.bd \(3\) \(39.127\) 3.3.257.1 None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{3}+(2-\beta _{1}-\beta _{2})q^{9}+(1-\beta _{2})q^{11}+\cdots\)
4900.2.a.be \(4\) \(39.127\) \(\Q(\sqrt{3}, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{2}q^{3}+(-2-\beta _{3})q^{11}+(2\beta _{1}-2\beta _{2}+\cdots)q^{13}+\cdots\)
4900.2.a.bf \(4\) \(39.127\) \(\Q(\sqrt{3}, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{2}q^{3}+(-2-\beta _{3})q^{11}+(2\beta _{1}-2\beta _{2}+\cdots)q^{13}+\cdots\)
4900.2.a.bg \(4\) \(39.127\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+\beta _{3}q^{9}+(-1-2\beta _{3})q^{11}+\cdots\)
4900.2.a.bh \(4\) \(39.127\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}-q^{11}+\beta _{1}q^{13}-3\beta _{1}q^{17}+\cdots\)
4900.2.a.bi \(4\) \(39.127\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+\beta _{3}q^{9}+(-1-2\beta _{3})q^{11}+\cdots\)
4900.2.a.bj \(4\) \(39.127\) \(\Q(\sqrt{5}, \sqrt{21})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(4+\beta _{3})q^{9}+(1-\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2450))\)\(^{\oplus 2}\)