Properties

Label 2700.2.a
Level $2700$
Weight $2$
Character orbit 2700.a
Rep. character $\chi_{2700}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $23$
Sturm bound $1080$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(1080\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2700))\).

Total New Old
Modular forms 594 25 569
Cusp forms 487 25 462
Eisenstein series 107 0 107

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

\(2\)\(3\)\(5\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(11\)
Minus space\(-\)\(14\)

Trace form

\( 25 q + q^{7} + O(q^{10}) \) \( 25 q + q^{7} + 13 q^{13} + q^{19} - 18 q^{31} + 7 q^{37} - 20 q^{43} + 12 q^{49} + 17 q^{61} - 5 q^{67} - 11 q^{73} + 31 q^{79} + 35 q^{91} + 37 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2700))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
2700.2.a.a \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(-\) \(+\) \(+\) \(q-5q^{7}-2q^{13}-q^{19}+11q^{31}-11q^{37}+\cdots\)
2700.2.a.b \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(-\) \(-\) \(+\) \(q-5q^{7}+7q^{13}-q^{19}-4q^{31}+q^{37}+\cdots\)
2700.2.a.c \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q-4q^{7}-7q^{13}+8q^{19}-7q^{31}+11q^{37}+\cdots\)
2700.2.a.d \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-3q^{11}+q^{13}+6q^{17}+2q^{19}+\cdots\)
2700.2.a.e \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-2q^{7}-2q^{11}+6q^{13}-q^{17}-3q^{19}+\cdots\)
2700.2.a.f \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-2q^{13}-3q^{17}+5q^{19}+3q^{23}+\cdots\)
2700.2.a.g \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-2q^{7}-2q^{13}+3q^{17}+5q^{19}-3q^{23}+\cdots\)
2700.2.a.h \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{7}+2q^{11}+6q^{13}+q^{17}-3q^{19}+\cdots\)
2700.2.a.i \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-2q^{7}+3q^{11}+q^{13}-6q^{17}+2q^{19}+\cdots\)
2700.2.a.j \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{7}+2q^{13}-7q^{19}-7q^{31}-q^{37}+\cdots\)
2700.2.a.k \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+q^{7}-6q^{11}+q^{13}-q^{19}+6q^{23}+\cdots\)
2700.2.a.l \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+q^{7}-2q^{13}-7q^{19}-7q^{31}+q^{37}+\cdots\)
2700.2.a.m \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(q+q^{7}+6q^{11}+q^{13}-q^{19}-6q^{23}+\cdots\)
2700.2.a.n \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{7}-3q^{11}-q^{13}-6q^{17}+2q^{19}+\cdots\)
2700.2.a.o \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}-2q^{11}-6q^{13}+q^{17}-3q^{19}+\cdots\)
2700.2.a.p \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{7}+2q^{11}-6q^{13}-q^{17}-3q^{19}+\cdots\)
2700.2.a.q \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{7}+3q^{11}-q^{13}+6q^{17}+2q^{19}+\cdots\)
2700.2.a.r \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+4q^{7}-6q^{11}+4q^{13}-3q^{17}-7q^{19}+\cdots\)
2700.2.a.s \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+4q^{7}+7q^{13}+8q^{19}-7q^{31}-11q^{37}+\cdots\)
2700.2.a.t \(1\) \(21.560\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+4q^{7}+6q^{11}+4q^{13}+3q^{17}-7q^{19}+\cdots\)
2700.2.a.u \(1\) \(21.560\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(-\) \(-\) \(-\) \(q+5q^{7}+2q^{13}-q^{19}+11q^{31}+11q^{37}+\cdots\)
2700.2.a.v \(2\) \(21.560\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{7}-\beta q^{11}-3q^{13}+2\beta q^{17}+3q^{19}+\cdots\)
2700.2.a.w \(2\) \(21.560\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{7}-\beta q^{11}+3q^{13}-2\beta q^{17}+3q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2700))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\)\(^{\oplus 2}\)